"Welcome to gVATTER, a Maple package for the enumeration of" "permutations avoiding generalized permutation patterns." "To see a list of available functions, type Help();" "or to learn more about a particular function type Help(function_name);" "There are ", 7411, " equivalence classes of generalized patterns of lengths ", [3, 5] "Class ", 1, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 1, 0]]} "Class ", 2, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]} "Class ", 3, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 3, 2, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 4, 1], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 3, 2, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 4, 3, 2, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 4, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 4, 3, 2, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3}, {}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {1, 2, 3, 4}, {}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 339, 1918, 12450, 90573, 733216, 6521621, 63314022, 665654185, 7538109717, 91451084129, 1183508002754, 16272940196258, 236915545781365, 3640799794963598, 58895141270431461] "" "Class ", 4, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 3, 2, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 4, 1], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 3, 2, 5], [0, 1, 1, 0]]} "Class ", 5, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 336, 1864, 11716, 81481, 623399, 5180773, 46542954, 448501857, 4617934373, 50537998712, 586033019325, 7172990781620, 92437248245405, 1250532005054472, 17722570047879973] "" "Class ", 6, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 3, 2, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 4, 1], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 3, 2, 5], [1, 1, 1, 1]]} "Class ", 7, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 1, 0]]} "Class ", 8, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 3, 5, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 3, 1, 2], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 3, 5, 4], [1, 1, 1, 1]]} "Class ", 9, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 3, 1, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 5, 2], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 3, 1, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 5, 3, 1, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 5, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 5, 3, 1, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {}, {}], [[2, 4, 3, 1, 5], {1, 2, 3}, {}], [[2, 5, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 341, 1943, 12732, 93503, 764671, 6870013, 67384275, 715697334, 8188372994, 100360573771, 1312187708535, 18227837321021, 268108835996827, 4162559625946030, 68028474467027442] "" "Class ", 10, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 3, 1, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 5, 2], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 3, 1, 4], [0, 1, 1, 0]]} "Class ", 11, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 3, 1, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 5, 2], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 3, 1, 4], [1, 0, 0, 1]]} "Class ", 12, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 3, 1, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 5, 2], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 3, 1, 4], [1, 1, 1, 1]]} "Class ", 13, " is:" {{[[1, 2, 3], [0, 0]], [[4, 1, 3, 5, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 3, 1, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 1, 3, 5, 2], [0, 1, 1, 0]]} "Class ", 14, " is:" {{[[1, 2, 3], [0, 0]], [[4, 1, 3, 5, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 3, 1, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 1, 3, 5, 2], [1, 1, 1, 1]]} "Class ", 15, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 5, 4], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 5, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 345, 1985, 13143, 97499, 805291, 7307863, 72392587, 776611144, 8973946737, 111090969015, 1466996277643, 20582289163709, 305766514890305, 4794715525757771, 79143381222447239] "" "Class ", 16, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 1, 0]]} "Class ", 17, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 5, 4], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [1, 0, 0, 1]]} "Class ", 18, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 5, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [1, 1, 1, 1]]} "Class ", 19, " is:" {{[[1, 2, 3], [0, 0]], [[5, 2, 3, 4, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 3, 2, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[5, 2, 3, 4, 1], [0, 1, 1, 0]]} "Class ", 20, " is:" {{[[1, 2, 3], [0, 0]], [[5, 2, 3, 4, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 3, 2, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[5, 2, 3, 4, 1], [1, 1, 1, 1]]} "Class ", 21, " is:" {{[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {}, {}], [[4, 3, 2, 1, 5], {1, 2, 3}, {}], [[5, 3, 2, 1, 4], {1, 2, 3}, {}], [[5, 4, 2, 1, 3], {1, 2, 3}, {}], [[5, 4, 3, 1, 2], {1, 2, 3}, {}], [[5, 4, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 338, 1935, 12662, 93074, 761123, 6841385, 67111659, 713042416, 8159758431, 100037830566, 1308290665050, 18178497419657, 267451267466053, 4153427980474617, 67896696952249538] "" "Class ", 22, " is:" {{[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 1, 0]]} "Class ", 23, " is:" {{[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {2}, {}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 330, 1795, 11051, 75393, 565726, 4620601, 40811111, 387320400, 3930113747, 42444959669, 486042070538, 5881219086683, 74973159244457, 1004201510674968, 14098287627274529] "" "Class ", 24, " is:" {{[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]} "Class ", 25, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 5, 4], [0, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 5, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [4, 5, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 128, 415, 1383, 4701, 16240, 56844, 201163, 718524, 2586995, 9378938, 34209292, 125447016, 462217843, 1710360047, 6353298947] "" "Class ", 26, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 5, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 1, 1, 0]]} "Class ", 27, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 5, 4], [1, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [1, 0, 0, 1]]} "Class ", 28, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 5, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [1, 1, 1, 1]]} "Class ", 29, " is:" {{[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]} "Class ", 30, " is:" {{[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 0]]} "Class ", 31, " is:" {{[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, %1], [[2, 4, 3, 1], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {1, 2}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, %1], [[4, 2, 1, 3], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1}, %1], [[4, 3, 2, 1], {2, 3}, {[1, 0, 0, 0, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[2, 5, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0]}], [[4, 1, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0]}]} %1 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 113, 283, 639, 1315, 2591, 4862, 8998, 16588, 30953, 57460, 107952, 201552, 380834, 714476, 1356600] "" "Class ", 32, " is:" {{[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]} "Class ", 33, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]} "Class ", 34, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[1, 2, 3, 4, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[1, 2, 3, 4, 5], [1, 1, 1, 0]]} "Class ", 35, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]} "Class ", 36, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3, 4, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[2, 1, 3, 4, 5], [0, 0, 1, 0]]} "Class ", 37, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 0]]} "Class ", 38, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 1, 0]]} "Class ", 39, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3, 4, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 3, 2, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[2, 1, 3, 4, 5], [1, 1, 1, 0]]} "Class ", 40, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 4, 3, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 1, 5, 3, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 1, 5, 4, 3], {3}, {}], [[3, 1, 5, 4, 2], {2, 3, 4}, {}], [[3, 2, 5, 4, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 70, 349, 2004, 13104, 95347, 764733, 6680866, 63135704, 640829806, 6950658942, 80175295422, 979749874205, 12639357424888, 171620382316675, 2446068991267418, 36507691859515650] "" "Class ", 41, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3, 4, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 3, 2, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[2, 1, 3, 4, 5], [1, 1, 0, 1]]} "Class ", 42, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 3, 5, 4], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3, 4, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 3, 1, 2], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 3, 5, 4], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[2, 1, 3, 4, 5], [0, 0, 1, 1]]} "Class ", 43, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 3, 5, 4], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 3, 5, 4], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 1]]} "Class ", 44, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 3, 5, 4], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 3, 5, 4], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 1, 1]]} "Class ", 45, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 3, 5, 4], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3, 4, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 3, 2, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 3, 5, 4], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[2, 1, 3, 4, 5], [1, 1, 1, 1]]} "Class ", 46, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[1, 3, 2, 4, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[1, 3, 2, 4, 5], [0, 0, 1, 0]]} "Class ", 47, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 0]]} "Class ", 48, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[1, 3, 2, 4, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 4, 2, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[1, 3, 2, 4, 5], [0, 1, 1, 0]]} "Class ", 49, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[1, 3, 2, 4, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 4, 2, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[1, 3, 2, 4, 5], [1, 1, 1, 0]]} "Class ", 50, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[1, 3, 2, 4, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 0, 0]]} {[[1, 2, 3], [0, 0]], [[1, 3, 2, 4, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[1, 3, 2, 4, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2, 4, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 70, 345, 1960, 12642, 91105, 725671, 6328937, 59983285, 613812142, 6744650921, 79201545712, 989808412843, 13116526993648, 183705369628311, 2711407530824344, 42062918652965790] "" "Class ", 51, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 3, 5, 2], {2, 3}, {}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 70, 345, 1947, 12388, 87191, 671694, 5606810, 50347210, 483264037, 4933162624, 53316757789, 607796825922, 7283964361254, 91502115973947, 1201786929556401, 16464851166340085] "" "Class ", 52, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[1, 3, 2, 4, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 4, 2, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[1, 3, 2, 4, 5], [0, 1, 0, 1]]} "Class ", 53, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[1, 3, 2, 4, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 4, 2, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[1, 3, 2, 4, 5], [1, 1, 0, 1]]} "Class ", 54, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 4, 3, 5], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[1, 3, 2, 4, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 2, 3, 1], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 4, 3, 5], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[1, 3, 2, 4, 5], [0, 0, 1, 1]]} "Class ", 55, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 1]]} "Class ", 56, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 4, 3, 5], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[1, 3, 2, 4, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 4, 2, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 2, 3, 1], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 4, 3, 5], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[1, 3, 2, 4, 5], [0, 1, 1, 1]]} "Class ", 57, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 4, 3, 5], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[1, 3, 2, 4, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 2, 3, 1], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 4, 3, 5], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[1, 3, 2, 4, 5], [1, 1, 1, 1]]} "Class ", 58, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 4, 2, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 1, 0]]} "Class ", 59, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 0]]} "Class ", 60, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2, 4, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 4, 2, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 1, 2, 4, 5], [0, 1, 1, 0]]} "Class ", 61, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2, 4, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 4, 2, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 1, 2, 4, 5], [1, 1, 1, 0]]} "Class ", 62, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2, 4, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 4, 2, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 1, 2, 4, 5], [0, 1, 0, 1]]} "Class ", 63, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2, 4, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 4, 2, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 1, 2, 4, 5], [1, 1, 0, 1]]} "Class ", 64, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 4, 5, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 4, 2, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 2, 1, 3], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 4, 5, 3], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 1, 1]]} "Class ", 65, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 1]]} "Class ", 66, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 4, 5, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2, 4, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 4, 2, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 2, 1, 3], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 4, 5, 3], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 1, 2, 4, 5], [0, 1, 1, 1]]} "Class ", 67, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 4, 5, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2, 4, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 4, 2, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 2, 1, 3], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 4, 5, 3], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 1, 2, 4, 5], [1, 1, 1, 1]]} "Class ", 68, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 5, 2, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 0]]} "Class ", 69, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 0]]} "Class ", 70, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1, 4, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 5, 2, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[2, 3, 1, 4, 5], [0, 1, 1, 0]]} "Class ", 71, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1, 4, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 5, 2, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[2, 3, 1, 4, 5], [1, 1, 1, 0]]} "Class ", 72, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 0, 0]]} {[[1, 2, 3], [0, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 70, 345, 1965, 12726, 92304, 741222, 6528636, 62578166, 648479427, 7224151627, 86094618260, 1092978232358, 14725210953326, 209834834690576, 3153298109327670, 49837921012973488] "" "Class ", 73, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {2, 3}, {[0, 0, 0, 1, 0, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 70, 345, 1947, 12388, 87191, 671694, 5606810, 50347210, 483264037, 4933162624, 53316757789, 607796825922, 7283964361254, 91502115973947, 1201786929556401, 16464851166340085] "" "Class ", 74, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1, 4, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 5, 2, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[2, 3, 1, 4, 5], [0, 1, 0, 1]]} "Class ", 75, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1, 4, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 5, 2, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[2, 3, 1, 4, 5], [1, 1, 0, 1]]} "Class ", 76, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 5, 3, 4], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 5, 2, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 1, 3, 2], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 5, 3, 4], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 1]]} "Class ", 77, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 5, 3, 4], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 5, 3, 4], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 1]]} "Class ", 78, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 5, 3, 4], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1, 4, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 5, 2, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 1, 3, 2], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 5, 3, 4], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[2, 3, 1, 4, 5], [0, 1, 1, 1]]} "Class ", 79, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 5, 3, 4], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1, 4, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 5, 2, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 1, 3, 2], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 5, 3, 4], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[2, 3, 1, 4, 5], [1, 1, 1, 1]]} "Class ", 80, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 1, 4, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 5, 2, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[3, 2, 1, 4, 5], [0, 0, 1, 0]]} "Class ", 81, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]} "Class ", 82, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 1, 4, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 5, 2, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 2, 1, 4, 5], [0, 1, 1, 0]]} "Class ", 83, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 1, 4, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 5, 2, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 2, 1, 4, 5], [1, 1, 1, 0]]} "Class ", 84, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 5, 2, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 0, 0]]} {[[1, 2, 3], [0, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 5, 2, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 70, 345, 1955, 12576, 90268, 716112, 6217007, 58647404, 597178176, 6528720833, 76266294556, 948060574396, 12495183123332, 174039626198068, 2554400188997709, 39403262961267390] "" "Class ", 85, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 70, 345, 1937, 12220, 84816, 641977, 5243019, 45919694, 428538375, 4242171775, 44351049555, 488023387517, 5633960918771, 68054320777555, 858025678737463, 11267158641879261] "" "Class ", 86, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 1, 4, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 5, 2, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 2, 1, 4, 5], [0, 1, 0, 1]]} "Class ", 87, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 1, 4, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 5, 2, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 2, 1, 4, 5], [1, 1, 0, 1]]} "Class ", 88, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 1, 4, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 5, 2, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[3, 2, 1, 4, 5], [0, 0, 1, 1]]} "Class ", 89, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2}, {[0, 0, 0, 1, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2}, {}], [[2, 4, 3, 5, 1], {2, 4}, {}], [[2, 5, 3, 4, 1], {2, 4}, {}], [[3, 4, 1, 5, 2], {1, 2}, {}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 70, 344, 1915, 11885, 80363, 586308, 4562508, 37631820, 326786222, 2974562683, 28257712258, 279263042230, 2862352636805, 30353835679285, 332277663065377, 3747718451772511] "" "Class ", 90, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 1, 4, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 5, 2, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 2, 1, 4, 5], [0, 1, 1, 1]]} "Class ", 91, " is:" {{[[1, 2, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 5, 2, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]} "Class ", 92, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {1, 2}, {}], [[1, 4, 3, 5, 2], {1, 2, 3, 4}, {}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 338, 1909, 12349, 89585, 722610, 6406153, 61969545, 649264469, 7326225958, 88567627281, 1142109532249, 15648112941377, 227008730231114, 3476179387182965, 56032373618661081] "" "Class ", 93, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 335, 1868, 11835, 83765, 655783, 5624698, 52463460, 528700385, 5724894504, 66289709971, 817380235501, 10692826974609, 147917997598494, 2157394149260183, 33087642892844607] "" "Class ", 94, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {3, 4}, {}], [[2, 1, 5, 4, 3], {3}, {}], [[3, 1, 5, 4, 2], {2, 3, 4}, {}], [[3, 2, 5, 4, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 336, 1871, 11837, 83321, 647738, 5499405, 50671761, 503154977, 5357307128, 60865558283, 734957610017, 9397768335897, 126850779540162, 1802263974532445, 26884018936945721] "" "Class ", 95, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 2, 3, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3, 5], [1, 1, 0, 0]]} "Class ", 96, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 4, 1, 2], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3, 5], [0, 0, 1, 0]]} "Class ", 97, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 4, 1, 2], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3, 5], [1, 0, 1, 0]]} "Class ", 98, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 4, 1, 2], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 1, 0]]} "Class ", 99, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 2, 3, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 4, 1, 2], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3, 5], [1, 1, 1, 0]]} "Class ", 100, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {}, {}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {2, 3}, {}], [[1, 4, 3, 5, 2], {2, 3}, {}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 335, 1860, 11717, 82137, 635608, 5372875, 49290073, 487447889, 5170222817, 58536719578, 704635614913, 8985589429273, 121006173821694, 1715959812465481, 25558682763736329] "" "Class ", 101, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 332, 1810, 11042, 73988, 539478, 4239126, 35664202, 319325811, 3028655105, 30302414864, 318719584395, 3513261173193, 40478422179291, 486312229107706, 6079494460747403] "" "Class ", 102, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {[0, 0, 0, 0, 1]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 1, 5, 4, 3], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 1, 5, 4, 2], {2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 2, 5, 4, 1], {2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 334, 1836, 11355, 77375, 576362, 4642820, 40204888, 371827901, 3656194521, 38054814624, 417824797401, 4823583652767, 58393919649724, 739433830495682, 9772951101678728] "" "Class ", 103, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3, 5], [1, 1, 0, 1]]} "Class ", 104, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 4, 1, 2], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3, 5], [0, 0, 1, 1]]} "Class ", 105, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 4, 1, 2], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3, 5], [1, 0, 1, 1]]} "Class ", 106, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 4, 1, 2], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 1, 1]]} "Class ", 107, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 2, 3, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 4, 1, 2], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2, 5, 4], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3, 5], [1, 1, 1, 1]]} "Class ", 108, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 4, 2, 5], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[1, 4, 2, 3, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 4, 3, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 2, 4, 1], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 4, 2, 5], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[1, 4, 2, 3, 5], [0, 0, 1, 0]]} "Class ", 109, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 4, 2, 5], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[1, 4, 2, 3, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 2, 4, 1], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 4, 2, 5], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[1, 4, 2, 3, 5], [1, 0, 1, 0]]} "Class ", 110, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 4, 2, 5], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[1, 4, 2, 3, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 4, 3, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 2, 4, 1], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 4, 2, 5], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[1, 4, 2, 3, 5], [0, 1, 1, 0]]} "Class ", 111, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 4, 2, 5], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[1, 4, 2, 3, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 4, 3, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 2, 4, 1], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 4, 2, 5], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[1, 4, 2, 3, 5], [1, 1, 1, 0]]} "Class ", 112, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[1, 4, 2, 3, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 4, 3, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 0, 0]]} {[[1, 2, 3], [0, 0]], [[1, 4, 2, 3, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[1, 4, 2, 3, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 4, 3, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 4, 2, 3, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 70, 346, 1976, 12841, 93422, 752462, 6646109, 63872676, 663543406, 7409404893, 88499951125, 1125902407123, 15199488347908, 217011544191108, 3267164920134617, 51728828847953785] "" "Class ", 113, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[1, 4, 2, 3, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[1, 4, 2, 3, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {2, 3}, {}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {2, 3}, {}], [[1, 4, 3, 5, 2], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {2, 3}, {}], [[1, 5, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 70, 346, 1970, 12722, 91534, 725695, 6277747, 58813061, 592908553, 6397877494, 73557882581, 897526624106, 11581927390072, 157577802166386, 2254237111648066, 33824061196857580] "" "Class ", 114, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[1, 4, 2, 3, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 4, 3, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[1, 4, 2, 3, 5], [0, 1, 0, 1]]} "Class ", 115, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[1, 4, 2, 3, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 4, 3, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[1, 4, 2, 3, 5], [1, 1, 0, 1]]} "Class ", 116, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 4, 2, 5], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[1, 4, 2, 3, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 4, 3, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 2, 4, 1], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 4, 2, 5], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[1, 4, 2, 3, 5], [0, 0, 1, 1]]} "Class ", 117, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 4, 2, 5], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[1, 4, 2, 3, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 2, 4, 1], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 4, 2, 5], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[1, 4, 2, 3, 5], [1, 0, 1, 1]]} "Class ", 118, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 4, 2, 5], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[1, 4, 2, 3, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 4, 3, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 2, 4, 1], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 4, 2, 5], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[1, 4, 2, 3, 5], [0, 1, 1, 1]]} "Class ", 119, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 4, 2, 5], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[1, 4, 2, 3, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 4, 3, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 2, 4, 1], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 4, 2, 5], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[1, 4, 2, 3, 5], [1, 1, 1, 1]]} "Class ", 120, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 4, 5, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 2, 3, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 4, 3, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 2, 1, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 4, 5, 2], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[4, 1, 2, 3, 5], [0, 0, 1, 0]]} "Class ", 121, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 4, 5, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 2, 1, 4], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 4, 5, 2], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 1, 0]]} "Class ", 122, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 4, 5, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 2, 3, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 4, 3, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 2, 1, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 4, 5, 2], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 1, 2, 3, 5], [0, 1, 1, 0]]} "Class ", 123, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 4, 5, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 2, 3, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 4, 3, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 2, 1, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 4, 5, 2], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 1, 2, 3, 5], [1, 1, 1, 0]]} "Class ", 124, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 2, 3, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 4, 3, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 1, 2, 3, 5], [0, 1, 0, 1]]} "Class ", 125, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 2, 3, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 4, 3, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 1, 2, 3, 5], [1, 1, 0, 1]]} "Class ", 126, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 4, 5, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 2, 3, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 4, 3, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 2, 1, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 4, 5, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[4, 1, 2, 3, 5], [0, 0, 1, 1]]} "Class ", 127, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 4, 5, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 2, 1, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 4, 5, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 1, 1]]} "Class ", 128, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 4, 5, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 2, 3, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 4, 3, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 2, 1, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 4, 5, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 1, 2, 3, 5], [0, 1, 1, 1]]} "Class ", 129, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 4, 5, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 2, 3, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 4, 3, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 2, 1, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 4, 5, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 1, 2, 3, 5], [1, 1, 1, 1]]} "Class ", 130, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 5, 2, 4], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 4, 1, 3, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 5, 3, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 1, 4, 2], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 5, 2, 4], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[2, 4, 1, 3, 5], [0, 0, 1, 0]]} "Class ", 131, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 5, 2, 4], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 4, 1, 3, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 5, 3, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 1, 4, 2], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 5, 2, 4], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[2, 4, 1, 3, 5], [1, 0, 1, 0]]} "Class ", 132, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 5, 2, 4], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 4, 1, 3, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 5, 3, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 1, 4, 2], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 5, 2, 4], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[2, 4, 1, 3, 5], [0, 1, 1, 0]]} "Class ", 133, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 5, 2, 4], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 4, 1, 3, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 5, 3, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 1, 4, 2], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 5, 2, 4], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[2, 4, 1, 3, 5], [1, 1, 1, 0]]} "Class ", 134, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 4, 1, 3, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 5, 3, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 0, 0]]} {[[1, 2, 3], [0, 0]], [[2, 4, 1, 3, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 4, 1, 3, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 5, 3, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 4, 1, 3, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 70, 346, 1980, 12914, 94482, 766449, 6827600, 66255189, 695690490, 7858747733, 95032323696, 1224854862797, 16762290086469, 242742328626445, 3708570089391779, 59612210463440013] "" "Class ", 135, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 4, 1, 3, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 5, 3, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 4, 1, 3, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 5, 3, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {2, 3}, {}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {2, 3}, {}], [[1, 4, 3, 5, 2], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {2, 3}, {}], [[1, 5, 3, 4, 2], {2, 3}, {[0, 0, 0, 1, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 70, 346, 1970, 12722, 91534, 725695, 6277747, 58813061, 592908553, 6397877494, 73557882581, 897526624106, 11581927390072, 157577802166386, 2254237111648066, 33824061196857580] "" "Class ", 136, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 4, 1, 3, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 5, 3, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[2, 4, 1, 3, 5], [0, 1, 0, 1]]} "Class ", 137, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 4, 1, 3, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 5, 3, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[2, 4, 1, 3, 5], [1, 1, 0, 1]]} "Class ", 138, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 5, 2, 4], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 4, 1, 3, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 5, 3, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 1, 4, 2], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 5, 2, 4], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[2, 4, 1, 3, 5], [0, 0, 1, 1]]} "Class ", 139, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 5, 2, 4], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 4, 1, 3, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 5, 3, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 1, 4, 2], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 5, 2, 4], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[2, 4, 1, 3, 5], [1, 0, 1, 1]]} "Class ", 140, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 5, 2, 4], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 4, 1, 3, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 5, 3, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 1, 4, 2], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 5, 2, 4], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[2, 4, 1, 3, 5], [0, 1, 1, 1]]} "Class ", 141, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 5, 2, 4], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 4, 1, 3, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 5, 3, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 1, 4, 2], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 5, 2, 4], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[2, 4, 1, 3, 5], [1, 1, 1, 1]]} "Class ", 142, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 5, 4, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 5, 3, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 1, 2, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 5, 4, 2], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3, 5], [0, 0, 1, 0]]} "Class ", 143, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 5, 4, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 1, 2, 4], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 5, 4, 2], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3, 5], [1, 0, 1, 0]]} "Class ", 144, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 5, 4, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 5, 3, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 1, 2, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 5, 4, 2], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3, 5], [0, 1, 1, 0]]} "Class ", 145, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 5, 4, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 5, 3, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 1, 2, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 5, 4, 2], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3, 5], [1, 1, 1, 0]]} "Class ", 146, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 5, 3, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 0, 0]]} {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 5, 3, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 70, 346, 1972, 12812, 93140, 750626, 6633742, 63839716, 664220158, 7431880754, 88967301146, 1134755407670, 15361676519206, 219992253744172, 3322717353464542, 52788270405478334] "" "Class ", 147, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {1, 2}, {[0, 1, 0, 0, 0, 0]}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {1, 2}, {[0, 1, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {1, 2}, {[0, 1, 0, 0, 0, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 70, 346, 1957, 12512, 88574, 687989, 5799394, 52694434, 512572309, 5310788015, 58334968985, 676707254429, 8261611588402, 105834499129201, 1418801149634479, 19857187969345043] "" "Class ", 148, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 5, 3, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3, 5], [0, 1, 0, 1]]} "Class ", 149, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 5, 3, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3, 5], [1, 1, 0, 1]]} "Class ", 150, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 5, 4, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 5, 3, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 1, 2, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 5, 4, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3, 5], [0, 0, 1, 1]]} "Class ", 151, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 5, 4, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 1, 2, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 5, 4, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3, 5], [1, 0, 1, 1]]} "Class ", 152, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 5, 4, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 5, 3, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 1, 2, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 5, 4, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3, 5], [0, 1, 1, 1]]} "Class ", 153, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 5, 4, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 5, 3, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 3, 1, 2, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 5, 4, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3, 5], [1, 1, 1, 1]]} "Class ", 154, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {1, 2}, {}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {1, 2, 3, 4}, {}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 338, 1913, 12403, 90268, 730487, 6499456, 63098542, 663552376, 7515175510, 91191571287, 1180333906775, 16232340438297, 236364607420705, 3632989451755885, 58779052599444103] "" "Class ", 155, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 335, 1869, 11853, 84001, 658655, 5658887, 52876834, 533839984, 5791196384, 67180295606, 829861110460, 10875411479843, 150705898097712, 2201798670018385, 33824779726520644] "" "Class ", 156, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 2, 4, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2, 5], [0, 1, 0, 0]]} "Class ", 157, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 2, 4, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2, 5], [1, 1, 0, 0]]} "Class ", 158, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 4, 1, 3], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2, 5], [0, 0, 1, 0]]} "Class ", 159, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 4, 1, 3], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2, 5], [1, 0, 1, 0]]} "Class ", 160, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 2, 4, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 4, 1, 3], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2, 5], [0, 1, 1, 0]]} "Class ", 161, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 2, 4, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 4, 1, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2, 5], [1, 1, 1, 0]]} "Class ", 162, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {}, {}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {2, 3}, {}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 336, 1877, 11939, 84784, 666593, 5740376, 53773177, 544171393, 5917424440, 68804359829, 851891334294, 11189526293650, 155408177040829, 2275549234409180, 35034731704149097] "" "Class ", 163, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 333, 1827, 11261, 76557, 568628, 4569807, 39465549, 364014451, 3568188582, 37010384025, 404707476857, 4650395213765, 55992713807090, 704636103919891, 9247119359682701] "" "Class ", 164, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 2, 4, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2, 5], [0, 1, 0, 1]]} "Class ", 165, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 2, 4, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2, 5], [1, 1, 0, 1]]} "Class ", 166, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 4, 1, 3], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2, 5], [0, 0, 1, 1]]} "Class ", 167, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 4, 1, 3], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2, 5], [1, 0, 1, 1]]} "Class ", 168, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 2, 4, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 4, 1, 3], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2, 5], [0, 1, 1, 1]]} "Class ", 169, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 2, 4, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 4, 1, 3], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 2, 5, 3], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2, 5], [1, 1, 1, 1]]} "Class ", 170, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 3, 2, 5], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 4, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 3, 2, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 4, 3, 2, 5], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 4, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 4, 3, 2, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 337, 1885, 12014, 85356, 671379, 5778476, 54087315, 546581241, 5933487170, 68843978233, 850318849081, 11138263897483, 154232956722999, 2251004180573175, 34536647175597460] "" "Class ", 171, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 3, 2, 5], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[1, 4, 3, 2, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 4, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 4, 1], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 3, 2, 5], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[1, 4, 3, 2, 5], [0, 1, 0, 0]]} "Class ", 172, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 3, 2, 5], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[1, 4, 3, 2, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 4, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 4, 1], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 3, 2, 5], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[1, 4, 3, 2, 5], [1, 1, 0, 0]]} "Class ", 173, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 3, 2, 5], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 4, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 3, 2, 5], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 1, 0]]} "Class ", 174, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 3, 2, 5], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[1, 4, 3, 2, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 4, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 4, 1], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 3, 2, 5], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[1, 4, 3, 2, 5], [1, 1, 1, 0]]} "Class ", 175, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[1, 4, 3, 2, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 4, 1], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[1, 4, 3, 2, 5], [1, 1, 0, 1]]} "Class ", 176, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 3, 4, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 1, 4], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 3, 4, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 1, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {1, 2}, {}], [[1, 4, 2, 5, 3], {1, 2}, {}], [[1, 4, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 338, 1915, 12423, 90535, 733478, 6535223, 63528515, 669000799, 7587120302, 92191004437, 1194895388881, 16455073145633, 239934910856994, 3692904773048109, 59830024335681625] "" "Class ", 177, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 1, 4], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 1, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 335, 1867, 11819, 83570, 653574, 5600078, 52183640, 525416316, 5684746526, 65776744394, 810518507674, 10596707638723, 146508570512409, 2135779092245271, 32741321856136153] "" "Class ", 178, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 3, 4, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 1, 4], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2, 5], [0, 1, 0, 0]]} "Class ", 179, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 3, 4, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 1, 4], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2, 5], [1, 1, 0, 0]]} "Class ", 180, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 3, 4, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 1, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2, 5], [0, 0, 1, 0]]} "Class ", 181, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 1, 4], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2, 5], [1, 0, 1, 0]]} "Class ", 182, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 3, 4, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 1, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2, 5], [0, 1, 1, 0]]} "Class ", 183, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 3, 4, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 1, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2, 5], [1, 1, 1, 0]]} "Class ", 184, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 3, 4, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 3, 4, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {}, {}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {2, 3}, {}], [[1, 4, 2, 5, 3], {2, 3}, {}], [[1, 4, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 336, 1880, 11975, 85243, 671814, 5802426, 54522263, 553632712, 6041785169, 70515713416, 876505587436, 11559759681183, 161224652814581, 2370914351130547, 36664484572552036] "" "Class ", 185, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 333, 1827, 11261, 76557, 568628, 4569807, 39465549, 364014451, 3568188582, 37010384025, 404707476857, 4650395213765, 55992713807090, 704636103919891, 9247119359682701] "" "Class ", 186, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 3, 4, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2, 5], [0, 1, 0, 1]]} "Class ", 187, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 3, 4, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2, 5], [1, 1, 0, 1]]} "Class ", 188, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 3, 4, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 1, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2, 5], [0, 0, 1, 1]]} "Class ", 189, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 1, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2, 5], [1, 0, 1, 1]]} "Class ", 190, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 3, 4, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 1, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2, 5], [0, 1, 1, 1]]} "Class ", 191, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 3, 4, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 3, 1, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 3, 5, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2, 5], [1, 1, 1, 1]]} "Class ", 192, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 5, 2, 3], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 4, 1, 2, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 5, 4, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 1, 4, 3], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 5, 2, 3], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[3, 4, 1, 2, 5], [0, 0, 1, 0]]} "Class ", 193, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 5, 2, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 4, 1, 2, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 5, 4, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 1, 4, 3], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 5, 2, 3], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[3, 4, 1, 2, 5], [1, 0, 1, 0]]} "Class ", 194, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 5, 2, 3], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 4, 1, 2, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 5, 4, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 1, 4, 3], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 5, 2, 3], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 4, 1, 2, 5], [0, 1, 1, 0]]} "Class ", 195, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 5, 2, 3], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 4, 1, 2, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 5, 4, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 1, 4, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 5, 2, 3], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 4, 1, 2, 5], [1, 1, 1, 0]]} "Class ", 196, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 5, 4, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 0, 0]]} {[[1, 2, 3], [0, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 5, 4, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 70, 347, 1996, 13116, 96871, 794428, 7164188, 70450457, 750340593, 8604058805, 105688236685, 1384520669157, 19267878488742, 283878143994102, 4414258407990341, 72245744277446438] "" "Class ", 197, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 4, 1, 2, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 5, 4, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 4, 1, 2, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 5, 4, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {2, 3}, {}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {2, 3}, {}], [[1, 4, 3, 5, 2], {2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {2, 3}, {}], [[1, 5, 3, 4, 2], {2, 3}, {[0, 0, 1, 0, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 70, 347, 1986, 12924, 93893, 752783, 6593289, 62590328, 639745585, 7001601436, 81662318543, 1010894094163, 13234257197490, 182657595900148, 2650371168550154, 40329278535847198] "" "Class ", 198, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 4, 1, 2, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 5, 4, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 4, 1, 2, 5], [0, 1, 0, 1]]} "Class ", 199, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 4, 1, 2, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 5, 4, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 4, 1, 2, 5], [1, 1, 0, 1]]} "Class ", 200, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 5, 2, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 4, 1, 2, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 5, 4, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 1, 4, 3], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 5, 2, 3], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[3, 4, 1, 2, 5], [0, 0, 1, 1]]} "Class ", 201, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 5, 2, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 4, 1, 2, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 5, 4, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 1, 4, 3], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 5, 2, 3], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[3, 4, 1, 2, 5], [1, 0, 1, 1]]} "Class ", 202, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 5, 2, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 4, 1, 2, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 5, 4, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 1, 4, 3], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 5, 2, 3], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 4, 1, 2, 5], [0, 1, 1, 1]]} "Class ", 203, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 5, 2, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 4, 1, 2, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 5, 4, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 1, 4, 3], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 5, 2, 3], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 4, 1, 2, 5], [1, 1, 1, 1]]} "Class ", 204, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 5, 3, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 5, 4, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 1, 3, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 5, 3, 2], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2, 5], [0, 0, 1, 0]]} "Class ", 205, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 5, 3, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 5, 4, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 1, 3, 4], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 5, 3, 2], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2, 5], [1, 0, 1, 0]]} "Class ", 206, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 5, 3, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 5, 4, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 1, 3, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 5, 3, 2], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2, 5], [0, 1, 1, 0]]} "Class ", 207, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 5, 3, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 5, 4, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 1, 3, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 5, 3, 2], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2, 5], [1, 1, 1, 0]]} "Class ", 208, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 5, 4, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 0, 0]]} {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 5, 4, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 70, 347, 1988, 13009, 95392, 776335, 6935486, 67522031, 711247064, 8061458929, 97811138186, 1265023237673, 17372220799600, 252464519434195, 3870856663815862, 62445166709079899] "" "Class ", 209, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 5, 4, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 5, 4, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {2, 3}, {}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {2, 3}, {}], [[1, 4, 3, 5, 2], {1, 2, 3, 4}, {[0, 1, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {2, 3}, {}], [[1, 5, 3, 4, 2], {1, 2, 3, 4}, {[0, 1, 0, 0, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 70, 347, 1978, 12823, 92628, 738587, 6430579, 60700330, 616965659, 6716641321, 77944848737, 960319120080, 12516384997238, 172033547213915, 2486555504119551, 37700151189941179] "" "Class ", 210, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 5, 4, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2, 5], [0, 1, 0, 1]]} "Class ", 211, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 5, 4, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2, 5], [1, 1, 0, 1]]} "Class ", 212, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 5, 3, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 5, 4, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 1, 3, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 5, 3, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2, 5], [0, 0, 1, 1]]} "Class ", 213, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 5, 3, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 5, 4, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 1, 3, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 5, 3, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2, 5], [1, 0, 1, 1]]} "Class ", 214, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 5, 3, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 5, 4, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 1, 3, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 5, 3, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2, 5], [0, 1, 1, 1]]} "Class ", 215, " is:" {{[[1, 2, 3], [0, 0]], [[1, 4, 5, 3, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 5, 4, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 2, 1, 3, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 4, 5, 3, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2, 5], [1, 1, 1, 1]]} "Class ", 216, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 2, 3, 4], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 4, 1, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 4, 3, 2], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 2, 3, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 5, 2, 3, 4], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 4, 1, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 4, 3, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 5, 2, 3, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 70, 346, 1976, 12837, 93353, 751416, 6631921, 63682598, 660980734, 7373994592, 87994707894, 1118424460996, 15084424921758, 215169255464324, 3236467025849391, 51196668359160654] "" "Class ", 217, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 2, 3, 4], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 4, 1, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 2, 5, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 4, 3, 2], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 2, 3, 4], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[2, 3, 4, 1, 5], [0, 1, 0, 0]]} "Class ", 218, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 2, 3, 4], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 4, 1, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 2, 5, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 4, 3, 2], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 2, 3, 4], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[2, 3, 4, 1, 5], [1, 1, 0, 0]]} "Class ", 219, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 2, 3, 4], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 4, 1, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 4, 3, 2], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 2, 3, 4], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[2, 3, 4, 1, 5], [1, 0, 1, 0]]} "Class ", 220, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 2, 3, 4], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 4, 1, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 2, 5, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 4, 3, 2], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 2, 3, 4], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[2, 3, 4, 1, 5], [0, 1, 1, 0]]} "Class ", 221, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 2, 3, 4], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 4, 1, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 2, 5, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 4, 3, 2], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 2, 3, 4], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[2, 3, 4, 1, 5], [1, 1, 1, 0]]} "Class ", 222, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 4, 1, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 4, 1, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 70, 346, 1973, 12755, 91944, 730024, 6325001, 59330969, 598774222, 6466618786, 74394605557, 908118681146, 11721372845983, 159486146716614, 2281359702830825, 34223905970261075] "" "Class ", 223, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 4, 1, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 2, 5, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[2, 3, 4, 1, 5], [0, 1, 0, 1]]} "Class ", 224, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 4, 1, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 2, 5, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[2, 3, 4, 1, 5], [1, 1, 0, 1]]} "Class ", 225, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 2, 3, 4], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 4, 1, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 4, 3, 2], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 2, 3, 4], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[2, 3, 4, 1, 5], [1, 0, 1, 1]]} "Class ", 226, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 2, 3, 4], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 4, 1, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 2, 5, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 4, 3, 2], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 2, 3, 4], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[2, 3, 4, 1, 5], [0, 1, 1, 1]]} "Class ", 227, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 2, 3, 4], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 4, 1, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 2, 5, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 4, 3, 2], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 2, 3, 4], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[2, 3, 4, 1, 5], [1, 1, 1, 1]]} "Class ", 228, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 4, 2, 3], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 4, 2, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 4, 2], {1, 2, 3, 4}, {}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 338, 1912, 12388, 90080, 728296, 6473593, 62785052, 659589939, 7462759529, 90463820043, 1169728615914, 16070190704675, 233766386929858, 3589412751996019, 58015163565862686] "" "Class ", 229, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 4, 2, 3], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 4, 2, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 336, 1886, 12063, 86444, 686648, 5986927, 56850560, 584003478, 6452973454, 76316779174, 961875490683, 12870760230918, 182225788332860, 2721611341766178, 42763776472226284] "" "Class ", 230, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 2, 5, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 4, 2, 3], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1, 5], [0, 1, 0, 0]]} "Class ", 231, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 2, 5, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 4, 2, 3], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1, 5], [1, 1, 0, 0]]} "Class ", 232, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 4, 2, 3], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1, 5], [0, 0, 1, 0]]} "Class ", 233, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 4, 2, 3], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1, 5], [1, 0, 1, 0]]} "Class ", 234, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 2, 5, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 4, 2, 3], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1, 5], [0, 1, 1, 0]]} "Class ", 235, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 4, 2, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1, 5], [1, 1, 1, 0]]} "Class ", 236, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 337, 1889, 12067, 86086, 680118, 5886574, 55429853, 563939570, 6165764379, 72089102330, 897566734343, 11856396376833, 165613818684235, 2439004705780289, 37770044884167663] "" "Class ", 237, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 335, 1863, 11729, 82173, 634120, 5340095, 48719001, 478551419, 5034604972, 56473436809, 672750504197, 8481798552521, 112825728286626, 1579130550013791, 23197459432043001] "" "Class ", 238, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 2, 5, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1, 5], [0, 1, 0, 1]]} "Class ", 239, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 2, 5, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1, 5], [1, 1, 0, 1]]} "Class ", 240, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 4, 2, 3], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1, 5], [0, 0, 1, 1]]} "Class ", 241, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 4, 2, 3], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1, 5], [1, 0, 1, 1]]} "Class ", 242, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 2, 5, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 4, 2, 3], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1, 5], [0, 1, 1, 1]]} "Class ", 243, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 4, 2, 3], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 2, 4, 3], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1, 5], [1, 1, 1, 1]]} "Class ", 244, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 5, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 4, 2], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 5, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 4, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 4, 3, 2, 5], {1, 2, 3}, {}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {1, 2, 3, 4}, {}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 340, 1931, 12597, 92118, 749863, 6706851, 65481694, 692343125, 7884974419, 96203016882, 1252093578323, 17313940970176, 253506434079795, 3917934526889648, 63738993074477629] "" "Class ", 245, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 5, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 4, 2], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 5, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 4, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 337, 1885, 12014, 85356, 671379, 5778476, 54087315, 546581241, 5933487170, 68843978233, 850318849081, 11138263897483, 154232956722999, 2251004180573175, 34536647175597460] "" "Class ", 246, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 5, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 4, 2], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1, 5], [0, 1, 0, 0]]} "Class ", 247, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 5, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 4, 2], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1, 5], [1, 1, 0, 0]]} "Class ", 248, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 5, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 4, 2], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1, 5], [0, 0, 1, 0]]} "Class ", 249, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 5, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 4, 2], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1, 5], [1, 0, 1, 0]]} "Class ", 250, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 5, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 4, 2], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1, 5], [0, 1, 1, 0]]} "Class ", 251, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 5, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 4, 2], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1, 5], [1, 1, 1, 0]]} "Class ", 252, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 5, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 5, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 4, 3, 2, 5], {2, 3, 4}, {}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {2, 3, 4}, {}], [[1, 5, 4, 3, 2], {2}, {}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 339, 1911, 12342, 89010, 713355, 6265070, 59989253, 620938307, 6916386516, 82429312749, 1047128189169, 14120095430873, 201476710965215, 3032421495421217, 48017232867818666] "" "Class ", 253, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 5, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 5, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 336, 1862, 11685, 81036, 617902, 5112694, 45711779, 438086792, 4484849242, 48778810866, 562061279830, 6834320225120, 87488184256964, 1175552871468578, 16547011964956525] "" "Class ", 254, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 5, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1, 5], [0, 1, 0, 1]]} "Class ", 255, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 5, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1, 5], [1, 1, 0, 1]]} "Class ", 256, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 5, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 4, 2], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1, 5], [0, 0, 1, 1]]} "Class ", 257, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 5, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 4, 2], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1, 5], [1, 0, 1, 1]]} "Class ", 258, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 5, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 4, 2], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1, 5], [0, 1, 1, 1]]} "Class ", 259, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 5, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 4, 2], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 3, 2, 4], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1, 5], [1, 1, 1, 1]]} "Class ", 260, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 3, 5, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 2, 4], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 3, 5, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 2, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {1, 2}, {}], [[1, 5, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 338, 1915, 12423, 90535, 733478, 6535223, 63528515, 669000799, 7587120302, 92191004437, 1194895388881, 16455073145633, 239934910856994, 3692904773048109, 59830024335681625] "" "Class ", 261, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 2, 4], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 2, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 336, 1885, 12047, 86249, 684380, 5960931, 56544074, 580261612, 6405243271, 75679471215, 952957776046, 12740022428517, 180219175823525, 2689402433728095, 42223769048898560] "" "Class ", 262, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 3, 5, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 2, 4], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1, 5], [0, 1, 0, 0]]} "Class ", 263, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 3, 5, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 2, 4], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1, 5], [1, 1, 0, 0]]} "Class ", 264, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 3, 5, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 2, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1, 5], [0, 0, 1, 0]]} "Class ", 265, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 2, 4], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1, 5], [1, 0, 1, 0]]} "Class ", 266, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 3, 5, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 2, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1, 5], [0, 1, 1, 0]]} "Class ", 267, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 3, 5, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 2, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1, 5], [1, 1, 1, 0]]} "Class ", 268, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 3, 5, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 3, 5, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {2, 3}, {}], [[1, 5, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 337, 1894, 12135, 87008, 691285, 6024670, 57160330, 586434417, 6469357939, 76363253721, 960352425152, 12819172892655, 181016328895533, 2695898646039523, 42232672609281074] "" "Class ", 269, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 335, 1863, 11729, 82173, 634120, 5340095, 48719001, 478551419, 5034604972, 56473436809, 672750504197, 8481798552521, 112825728286626, 1579130550013791, 23197459432043001] "" "Class ", 270, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 3, 5, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1, 5], [0, 1, 0, 1]]} "Class ", 271, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 3, 5, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1, 5], [1, 1, 0, 1]]} "Class ", 272, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 3, 5, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 2, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1, 5], [0, 0, 1, 1]]} "Class ", 273, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 2, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1, 5], [1, 0, 1, 1]]} "Class ", 274, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 3, 5, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 2, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1, 5], [0, 1, 1, 1]]} "Class ", 275, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 3, 5, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 3, 2, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 3, 4, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1, 5], [1, 1, 1, 1]]} "Class ", 276, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 5, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 4, 3], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 5, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 4, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 4, 3, 2, 5], {1, 2, 3}, {}], [[1, 5, 3, 2, 4], {1, 2, 3}, {}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {1, 2, 3, 4}, {}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 341, 1944, 12740, 93616, 765899, 6885117, 67565503, 718029974, 8219341584, 100795737127, 1318578892141, 18326592727931, 269706114891487, 4189626272265212, 68507704040192559] "" "Class ", 277, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 5, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 4, 3], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 5, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 4, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {[0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 337, 1885, 12014, 85356, 671379, 5778476, 54087315, 546581241, 5933487170, 68843978233, 850318849081, 11138263897483, 154232956722999, 2251004180573175, 34536647175597460] "" "Class ", 278, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 5, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 4, 3], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1, 5], [0, 1, 0, 0]]} "Class ", 279, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 5, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 4, 3], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1, 5], [1, 1, 0, 0]]} "Class ", 280, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 5, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 4, 3], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1, 5], [0, 0, 1, 0]]} "Class ", 281, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 5, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 4, 3], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1, 5], [1, 0, 1, 0]]} "Class ", 282, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 5, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 4, 3], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1, 5], [0, 1, 1, 0]]} "Class ", 283, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 5, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 4, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1, 5], [1, 1, 1, 0]]} "Class ", 284, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 5, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 5, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 4, 3, 2, 5], {2, 3, 4}, {}], [[1, 5, 3, 2, 4], {2, 3, 4}, {}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 340, 1925, 12512, 90944, 735504, 6525808, 63179113, 661759169, 7463517678, 90121134603, 1160450251579, 15869009581439, 229711897781218, 3508762012868799, 56402606105078026] "" "Class ", 285, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 5, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 5, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {2}, {[0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 336, 1862, 11685, 81036, 617902, 5112694, 45711779, 438086792, 4484849242, 48778810866, 562061279830, 6834320225120, 87488184256964, 1175552871468578, 16547011964956525] "" "Class ", 286, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 5, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1, 5], [0, 1, 0, 1]]} "Class ", 287, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 5, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1, 5], [1, 1, 0, 1]]} "Class ", 288, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 5, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 4, 3], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1, 5], [0, 0, 1, 1]]} "Class ", 289, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 5, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 4, 3], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1, 5], [1, 0, 1, 1]]} "Class ", 290, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 5, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 4, 3], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1, 5], [0, 1, 1, 1]]} "Class ", 291, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 5, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 4, 3], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 4, 2, 3], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1, 5], [1, 1, 1, 1]]} "Class ", 292, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 4, 3, 2, 5], {1, 2, 3}, {}], [[1, 5, 3, 2, 4], {1, 2, 3}, {}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 338, 1915, 12423, 90535, 733478, 6535223, 63528515, 669000799, 7587120302, 92191004437, 1194895388881, 16455073145633, 239934910856994, 3692904773048109, 59830024335681625] "" "Class ", 293, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 334, 1855, 11695, 82275, 640152, 5454139, 50535249, 505820565, 5440256114, 62568015646, 766296946813, 9957127950381, 136816642222702, 1982107882318900, 30195914485366800] "" "Class ", 294, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 5, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 3, 4], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1, 5], [0, 1, 0, 0]]} "Class ", 295, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 5, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 3, 4], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1, 5], [1, 1, 0, 0]]} "Class ", 296, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 5, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 3, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1, 5], [0, 0, 1, 0]]} "Class ", 297, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 5, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 3, 4], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1, 5], [1, 0, 1, 0]]} "Class ", 298, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 5, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 3, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1, 5], [0, 1, 1, 0]]} "Class ", 299, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 5, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 3, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1, 5], [1, 1, 1, 0]]} "Class ", 300, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 4, 3, 2, 5], {2, 3, 4}, {}], [[1, 5, 3, 2, 4], {2, 3, 4}, {}], [[1, 5, 4, 2, 3], {2, 3, 4}, {}], [[1, 5, 4, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 338, 1906, 12269, 88464, 707137, 6205371, 59299935, 613095748, 6817880018, 81151492493, 1029391764406, 13862843513917, 197535694466041, 2969266427115557, 46955584457011062] "" "Class ", 301, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 334, 1846, 11516, 79664, 605206, 5001697, 44654937, 428058397, 4383510889, 47744259518, 551001806097, 6715353876063, 86176147434562, 1161350366516849, 16397190852734079] "" "Class ", 302, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 5, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1, 5], [0, 1, 0, 1]]} "Class ", 303, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 5, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1, 5], [1, 1, 0, 1]]} "Class ", 304, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 5, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]} "Class ", 305, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 5, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1, 5], [1, 0, 1, 1]]} "Class ", 306, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 5, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 3, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1, 5], [0, 1, 1, 1]]} "Class ", 307, " is:" {{[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 5, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]} "Class ", 308, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 3, 5, 4], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 3, 5, 4], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 1, 3, 5, 4], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 4, 3, 5], {3, 5}, {}], [[2, 1, 5, 3, 4], {3, 5}, {}], [[2, 1, 5, 4, 3], {3}, {}], [[3, 1, 5, 4, 2], {2, 3, 4}, {}], [[3, 2, 5, 4, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 70, 346, 1969, 12731, 91889, 732956, 6397405, 60648439, 620381836, 6809880548, 79832672627, 995348919593, 13150225705261, 183502492226974, 2696762546013505, 41629611950293241] "" "Class ", 309, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 3, 5, 4], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3, 5, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 3, 1, 2], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 3, 5, 4], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[2, 1, 3, 5, 4], [1, 1, 0, 0]]} "Class ", 310, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3, 5, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3, 5, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 4, 3, 5], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 1, 5, 3, 4], {3, 4}, {[0, 0, 0, 1, 0, 0]}], [[2, 1, 5, 4, 3], {3}, {}], [[3, 1, 5, 4, 2], {2, 3, 4}, {}], [[3, 2, 5, 4, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 70, 346, 1960, 12574, 89535, 701468, 5982172, 55170973, 546570273, 5787998382, 65212590916, 778775473702, 9823404766597, 130493002155673, 1820582574972877, 26612732666401665] "" "Class ", 311, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3, 5, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 3, 1, 2], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[2, 1, 3, 5, 4], [1, 1, 1, 0]]} "Class ", 312, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 3, 5, 4], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3, 5, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 3, 1, 2], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 3, 5, 4], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[2, 1, 3, 5, 4], [1, 1, 0, 1]]} "Class ", 313, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 4, 5, 3], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2, 5, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 4, 1, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 2, 1, 3], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 4, 5, 3], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 1, 2, 5, 4], [0, 1, 0, 0]]} "Class ", 314, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 4, 5, 3], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2, 5, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 4, 1, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 2, 1, 3], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 4, 5, 3], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 1, 2, 5, 4], [1, 1, 0, 0]]} "Class ", 315, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2, 5, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 4, 1, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[3, 1, 2, 5, 4], [0, 0, 1, 0]]} "Class ", 316, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2, 5, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2, 5, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 4, 3, 5], {3, 4}, {[0, 0, 1, 0, 0, 0]}], [[2, 1, 5, 3, 4], {3, 4}, {[0, 0, 1, 0, 0, 0]}], [[2, 1, 5, 4, 3], {3}, {}], [[3, 1, 5, 4, 2], {2, 3, 4}, {}], [[3, 2, 5, 4, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 70, 347, 1979, 12828, 92579, 736817, 6395002, 60103725, 607432029, 6566931990, 75576634337, 922254235189, 11890202868698, 161458388245615, 2302776504226015, 34410396076219432] "" "Class ", 317, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2, 5, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 4, 1, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 1, 2, 5, 4], [0, 1, 1, 0]]} "Class ", 318, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2, 5, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 4, 1, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 1, 2, 5, 4], [1, 1, 1, 0]]} "Class ", 319, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 4, 5, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2, 5, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 4, 1, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 2, 1, 3], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 4, 5, 3], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 1, 2, 5, 4], [0, 1, 0, 1]]} "Class ", 320, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 4, 5, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2, 5, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 4, 1, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 2, 1, 3], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 4, 5, 3], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 1, 2, 5, 4], [1, 1, 0, 1]]} "Class ", 321, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 4, 5, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2, 5, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 4, 1, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 2, 1, 3], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 4, 5, 3], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[3, 1, 2, 5, 4], [0, 0, 1, 1]]} "Class ", 322, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 4, 5, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2, 5, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 2, 1, 3], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 4, 5, 3], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[3, 1, 2, 5, 4], [1, 0, 1, 1]]} "Class ", 323, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 4, 5, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2, 5, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 4, 1, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 2, 1, 3], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 4, 5, 3], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 1, 2, 5, 4], [0, 1, 1, 1]]} "Class ", 324, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 4, 5, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2, 5, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 4, 1, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 2, 1, 3], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 4, 5, 3], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 1, 2, 5, 4], [1, 1, 1, 1]]} "Class ", 325, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1, 5, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 3, 2], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1, 5, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 3, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {}], [[2, 1, 4, 3, 5], {1, 2}, {}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {1, 2, 3}, {}], [[3, 1, 5, 4, 2], {1, 2, 3}, {}], [[3, 2, 5, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 339, 1922, 12496, 91150, 739605, 6596721, 64209363, 676934963, 7686437202, 93506735783, 1213395167477, 16729534575901, 244226440547193, 3763402603811758, 61044439259239792] "" "Class ", 326, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1, 5, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1, 5, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 335, 1859, 11699, 81888, 632499, 5334959, 48825101, 481615098, 5094747190, 57524361581, 690526504117, 8781042244741, 117920621027207, 1667540226627565, 24768692755200107] "" "Class ", 327, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1, 5, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 5, 1, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 3, 2], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[2, 3, 1, 5, 4], [0, 1, 0, 0]]} "Class ", 328, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1, 5, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 5, 1, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 3, 2], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[2, 3, 1, 5, 4], [1, 1, 0, 0]]} "Class ", 329, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1, 5, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1, 5, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 4, 3, 5], {3, 4}, {}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {3}, {}], [[3, 1, 5, 4, 2], {2, 3, 4}, {}], [[3, 2, 5, 4, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 338, 1899, 12179, 87163, 691114, 5999035, 56640651, 577420447, 6322981898, 73995393317, 921643045177, 12171565839785, 169879625526122, 2498372902949925, 38614535300783065] "" "Class ", 330, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {[0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 4, 3, 5], {3, 4}, {[0, 0, 0, 1, 0, 0]}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 1, 5, 4, 2], {2, 3, 4}, {[0, 0, 0, 0, 1, 0]}], [[3, 2, 5, 4, 1], {2, 3, 4}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 334, 1835, 11338, 77146, 573629, 4611156, 39840047, 367560655, 3605150501, 37426609777, 409851850306, 4719056329564, 56977738458898, 719602247587449, 9485997859915558] "" "Class ", 331, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1, 5, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 5, 1, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[2, 3, 1, 5, 4], [0, 1, 1, 0]]} "Class ", 332, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1, 5, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 5, 1, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[2, 3, 1, 5, 4], [1, 1, 1, 0]]} "Class ", 333, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1, 5, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 3, 2], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [1, 0, 0, 0]]} {[[1, 2, 3], [0, 0]], [[2, 3, 1, 5, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1, 5, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 3, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 3, 1, 5, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 336, 1885, 12047, 86248, 684360, 5960630, 56539894, 580205501, 6404482470, 75668931848, 952806941668, 12737783216526, 180184603253492, 2688846759764663, 42214470409767469] "" "Class ", 334, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1, 5, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 3, 2], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [1, 0, 0, 1]]} {[[1, 2, 3], [0, 0]], [[2, 3, 1, 5, 4], [1, 0, 0, 1]]} "Class ", 335, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1, 5, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 5, 1, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 3, 2], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[2, 3, 1, 5, 4], [0, 1, 0, 1]]} "Class ", 336, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1, 5, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 5, 1, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 3, 2], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[2, 3, 1, 5, 4], [1, 1, 0, 1]]} "Class ", 337, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1, 5, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 3, 2], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[2, 3, 1, 5, 4], [0, 0, 1, 1]]} "Class ", 338, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 3, 2], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 1]]} "Class ", 339, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1, 5, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 5, 1, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 3, 2], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[2, 3, 1, 5, 4], [0, 1, 1, 1]]} "Class ", 340, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1, 5, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 5, 1, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 3, 2], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 5, 3, 4], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[2, 3, 1, 5, 4], [1, 1, 1, 1]]} "Class ", 341, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 1, 5, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 5, 1, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 1, 5, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 5, 1, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {}], [[2, 1, 4, 3, 5], {1, 2}, {}], [[2, 1, 5, 3, 4], {1, 2, 3}, {}], [[2, 1, 5, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 5, 4, 2], {1, 2, 3}, {}], [[3, 2, 5, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 337, 1900, 12260, 88805, 715106, 6331464, 61164514, 640055431, 7213413146, 87100041851, 1121837113076, 15352107588972, 222449291667862, 3402315574010134, 54776571422705960] "" "Class ", 342, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 1, 5, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 1, 5, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {[0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 333, 1836, 11453, 79436, 607453, 5072252, 45946096, 448631334, 4698330054, 52529221215, 624535470687, 7868036238947, 104705331712018, 1467683570002550, 21614807678443882] "" "Class ", 343, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 1, 5, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 5, 1, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 2, 3], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 2, 1, 5, 4], [0, 1, 0, 0]]} "Class ", 344, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 1, 5, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 5, 1, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 2, 3], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 2, 1, 5, 4], [1, 1, 0, 0]]} "Class ", 345, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 1, 5, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 5, 1, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 1, 5, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 5, 1, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 4, 3, 5], {3, 4}, {}], [[2, 1, 5, 3, 4], {3, 4}, {}], [[2, 1, 5, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 5, 4, 2], {2, 3, 4}, {}], [[3, 2, 5, 4, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 337, 1886, 12024, 85450, 671899, 5778195, 53998949, 544441087, 5892002508, 68099495387, 837221480927, 10907509333413, 150108284312611, 2175726849783956, 33128094452736318] "" "Class ", 346, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 1, 5, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 1, 5, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {[0, 0, 1, 0, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 4, 3, 5], {3, 4}, {[0, 0, 1, 0, 0, 0]}], [[2, 1, 5, 3, 4], {3, 4}, {[0, 0, 1, 0, 0, 0]}], [[2, 1, 5, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 5, 4, 2], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}], [[3, 2, 5, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 333, 1827, 11267, 76668, 570390, 4594695, 39808001, 368687312, 3632513314, 37910359763, 417567159365, 4838620272836, 58819104937430, 748222663967315, 9937658412912223] "" "Class ", 347, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 1, 5, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 5, 1, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 2, 1, 5, 4], [0, 1, 1, 0]]} "Class ", 348, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 1, 5, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 5, 1, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 2, 1, 5, 4], [1, 1, 1, 0]]} "Class ", 349, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 1, 5, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 2, 3], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [1, 0, 0, 0]]} {[[1, 2, 3], [0, 0]], [[3, 2, 1, 5, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 1, 5, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 2, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[3, 2, 1, 5, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 334, 1855, 11699, 82348, 641119, 5466016, 50677665, 507548066, 5461773596, 62845801092, 770030054523, 10009477996094, 137583242150598, 1993830316369059, 30382984347802874] "" "Class ", 350, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 1, 5, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 2, 3], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [1, 0, 0, 1]]} {[[1, 2, 3], [0, 0]], [[3, 2, 1, 5, 4], [1, 0, 0, 1]]} "Class ", 351, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 1, 5, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 5, 1, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 2, 3], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 2, 1, 5, 4], [0, 1, 0, 1]]} "Class ", 352, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 1, 5, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 5, 1, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 2, 3], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 2, 1, 5, 4], [1, 1, 0, 1]]} "Class ", 353, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 1, 5, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 5, 1, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 2, 3], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[3, 2, 1, 5, 4], [0, 0, 1, 1]]} "Class ", 354, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 1, 5, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 2, 3], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[3, 2, 1, 5, 4], [1, 0, 1, 1]]} "Class ", 355, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 1, 5, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 5, 1, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 2, 3], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 2, 1, 5, 4], [0, 1, 1, 1]]} "Class ", 356, " is:" {{[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 1, 5, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 5, 1, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 5, 1, 2, 3], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 1, 5, 4, 3], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 2, 1, 5, 4], [1, 1, 1, 1]]} "Class ", 357, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 4, 5, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 2, 3, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 4, 3, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 2, 1, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 4, 5, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 1, 2, 3, 4], [0, 0, 1, 0]]} "Class ", 358, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 4, 5, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 2, 1, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 4, 5, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 1, 0]]} "Class ", 359, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 4, 5, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 2, 3, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 4, 3, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 2, 1, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 4, 5, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 1, 2, 3, 4], [0, 1, 1, 0]]} "Class ", 360, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 4, 5, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 2, 3, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 4, 3, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 2, 1, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 4, 5, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 1, 2, 3, 4], [1, 1, 1, 0]]} "Class ", 361, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 4, 5, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 2, 3, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 4, 3, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 2, 1, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 4, 5, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 1, 2, 3, 4], [0, 1, 0, 1]]} "Class ", 362, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 4, 5, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 2, 1, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 4, 5, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]} "Class ", 363, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 4, 5, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 2, 3, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 4, 3, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 2, 1, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 4, 5, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 1, 2, 3, 4], [0, 0, 1, 1]]} "Class ", 364, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 4, 5, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 2, 1, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 4, 5, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 1, 1]]} "Class ", 365, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 4, 5, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 2, 3, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 4, 3, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 2, 1, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 4, 5, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 1, 2, 3, 4], [0, 1, 1, 1]]} "Class ", 366, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 4, 5, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 4, 5, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]} "Class ", 367, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 5, 1, 4], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 5, 1, 3, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 5, 3, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 1, 5, 2], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 5, 1, 4], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[2, 5, 1, 3, 4], [0, 0, 1, 0]]} "Class ", 368, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 5, 1, 4], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 5, 1, 3, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 5, 3, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 1, 5, 2], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 5, 1, 4], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[2, 5, 1, 3, 4], [1, 0, 1, 0]]} "Class ", 369, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 5, 1, 4], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 5, 1, 3, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 5, 3, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 1, 5, 2], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 5, 1, 4], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[2, 5, 1, 3, 4], [0, 1, 1, 0]]} "Class ", 370, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 5, 1, 4], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 5, 1, 3, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 5, 3, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 1, 5, 2], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 5, 1, 4], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[2, 5, 1, 3, 4], [1, 1, 1, 0]]} "Class ", 371, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 5, 1, 4], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 5, 1, 3, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 5, 3, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 1, 5, 2], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 5, 1, 4], [1, 0, 0, 0]]} {[[1, 2, 3], [0, 0]], [[2, 5, 1, 3, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 3, 5, 1, 4], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 5, 1, 3, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 5, 3, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 1, 5, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 5, 1, 3, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 70, 346, 1980, 12907, 94387, 765174, 6812111, 66063006, 693249213, 7826501619, 94587760643, 1218446093472, 16665624274494, 241217502000739, 3683434619652613, 59179686048775853] "" "Class ", 372, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 5, 1, 4], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 5, 1, 3, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 5, 3, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 1, 5, 2], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 5, 1, 4], [1, 0, 0, 1]]} {[[1, 2, 3], [0, 0]], [[2, 5, 1, 3, 4], [1, 0, 0, 1]]} "Class ", 373, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 5, 1, 4], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 5, 1, 3, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 5, 3, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 1, 5, 2], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 5, 1, 4], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[2, 5, 1, 3, 4], [0, 1, 0, 1]]} "Class ", 374, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 5, 1, 4], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 5, 1, 3, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 5, 3, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 1, 5, 2], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 5, 1, 4], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[2, 5, 1, 3, 4], [1, 1, 0, 1]]} "Class ", 375, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 5, 1, 4], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 5, 1, 3, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 5, 3, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 1, 5, 2], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 5, 1, 4], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[2, 5, 1, 3, 4], [0, 0, 1, 1]]} "Class ", 376, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 5, 1, 4], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 5, 1, 3, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 5, 3, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 1, 5, 2], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 5, 1, 4], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[2, 5, 1, 3, 4], [1, 0, 1, 1]]} "Class ", 377, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 5, 1, 4], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 5, 1, 3, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 5, 3, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 1, 5, 2], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 5, 1, 4], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[2, 5, 1, 3, 4], [0, 1, 1, 1]]} "Class ", 378, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 5, 1, 4], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 5, 1, 3, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 5, 3, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 1, 5, 2], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 5, 1, 4], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[2, 5, 1, 3, 4], [1, 1, 1, 1]]} "Class ", 379, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 5, 4, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 1, 3, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 5, 3, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 1, 2, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 5, 4, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 2, 1, 3, 4], [0, 0, 1, 0]]} "Class ", 380, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 5, 4, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 1, 2, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 5, 4, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 1, 0]]} "Class ", 381, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 5, 4, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 1, 3, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 5, 3, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 1, 2, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 5, 4, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 2, 1, 3, 4], [0, 1, 1, 0]]} "Class ", 382, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 5, 4, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 1, 3, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 5, 3, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 1, 2, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 5, 4, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 2, 1, 3, 4], [1, 1, 1, 0]]} "Class ", 383, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 5, 4, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 1, 3, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 5, 3, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 1, 2, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 5, 4, 1], [1, 0, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 2, 1, 3, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 3, 5, 4, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 1, 3, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 5, 3, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 1, 2, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 2, 1, 3, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 70, 346, 1972, 12830, 93359, 753413, 6666520, 64242211, 669260296, 7498074980, 89872503314, 1147733204984, 15556138014082, 223041395378725, 3372647790438346, 53641734874779425] "" "Class ", 384, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 5, 4, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 1, 2, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 5, 4, 1], [1, 0, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 3, 5, 4, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 1, 2, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {2}, {}], [[4, 2, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 70, 346, 1957, 12512, 88574, 687989, 5799394, 52694434, 512572309, 5310788015, 58334968985, 676707254429, 8261611588402, 105834499129201, 1418801149634479, 19857187969345043] "" "Class ", 385, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 5, 4, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 1, 3, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 5, 3, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 1, 2, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 5, 4, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 2, 1, 3, 4], [0, 1, 0, 1]]} "Class ", 386, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 5, 4, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 1, 3, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 5, 3, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 1, 2, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 5, 4, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 2, 1, 3, 4], [1, 1, 0, 1]]} "Class ", 387, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 5, 4, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 1, 3, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 5, 3, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 1, 2, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 5, 4, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 2, 1, 3, 4], [0, 0, 1, 1]]} "Class ", 388, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 5, 4, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 1, 2, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 5, 4, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 1, 1]]} "Class ", 389, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 5, 4, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 1, 3, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 5, 3, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 1, 2, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 5, 4, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 2, 1, 3, 4], [0, 1, 1, 1]]} "Class ", 390, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 5, 4, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 1, 3, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 5, 3, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 3, 1, 2, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 5, 4, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 2, 1, 3, 4], [1, 1, 1, 1]]} "Class ", 391, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 1, 5, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 5, 2, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 1, 4, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 1, 5, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 4, 1, 5, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 5, 2, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 1, 4, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 4, 1, 5, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4}, {}], [[3, 4, 2, 5, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 339, 1925, 12532, 91608, 744752, 6657299, 64934507, 686072920, 7806810237, 95176318604, 1237708843622, 17101500999920, 250192845540864, 3863633866168265, 62804933717773669] "" "Class ", 392, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 1, 5, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 5, 2, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 1, 4, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 1, 5, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 4, 1, 5, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 5, 2, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 1, 4, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 4, 1, 5, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 336, 1886, 12063, 86443, 686628, 5986632, 56846516, 583949660, 6452247993, 76306760666, 961732343716, 12868636133033, 182192985240568, 2721083737649985, 42754938755060969] "" "Class ", 393, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 1, 5, 3], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 5, 2, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 1, 4, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 5, 1, 3], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 1, 5, 3], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 1, 5, 2, 4], [0, 1, 0, 0]]} "Class ", 394, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 1, 5, 3], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 5, 2, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 1, 4, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 5, 1, 3], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 1, 5, 3], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 1, 5, 2, 4], [1, 1, 0, 0]]} "Class ", 395, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 1, 5, 3], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 5, 2, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 1, 4, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 5, 1, 3], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 1, 5, 3], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[3, 1, 5, 2, 4], [0, 0, 1, 0]]} "Class ", 396, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 1, 5, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 5, 2, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 1, 4, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 5, 1, 3], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 1, 5, 3], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[3, 1, 5, 2, 4], [1, 0, 1, 0]]} "Class ", 397, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 1, 5, 3], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 5, 2, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 1, 4, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 5, 1, 3], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 1, 5, 3], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 1, 5, 2, 4], [0, 1, 1, 0]]} "Class ", 398, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 1, 5, 3], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 5, 2, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 1, 4, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 5, 1, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 1, 5, 3], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 1, 5, 2, 4], [1, 1, 1, 0]]} "Class ", 399, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 1, 5, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 5, 2, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 1, 4, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 5, 1, 3], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 1, 5, 3], [1, 0, 0, 0]]} {[[1, 2, 3], [0, 0]], [[3, 1, 5, 2, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 4, 1, 5, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 5, 2, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 1, 4, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 5, 1, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[3, 1, 5, 2, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 336, 1876, 11922, 84561, 663936, 5709172, 53401066, 539592700, 5858858167, 68022813628, 840994098651, 11030727791214, 152990578116606, 2237126536567174, 34397893022095661] "" "Class ", 400, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 1, 5, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 5, 2, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 1, 4, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 5, 1, 3], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 1, 5, 3], [1, 0, 0, 1]]} {[[1, 2, 3], [0, 0]], [[3, 1, 5, 2, 4], [1, 0, 0, 1]]} "Class ", 401, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 1, 5, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 5, 2, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 1, 4, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 5, 1, 3], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 1, 5, 3], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 1, 5, 2, 4], [0, 1, 0, 1]]} "Class ", 402, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 1, 5, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 5, 2, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 1, 4, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 5, 1, 3], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 1, 5, 3], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 1, 5, 2, 4], [1, 1, 0, 1]]} "Class ", 403, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 1, 5, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 5, 2, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 1, 4, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 5, 1, 3], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 1, 5, 3], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[3, 1, 5, 2, 4], [0, 0, 1, 1]]} "Class ", 404, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 1, 5, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 5, 2, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 1, 4, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 5, 1, 3], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 1, 5, 3], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[3, 1, 5, 2, 4], [1, 0, 1, 1]]} "Class ", 405, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 1, 5, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 5, 2, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 1, 4, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 5, 1, 3], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 1, 5, 3], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 1, 5, 2, 4], [0, 1, 1, 1]]} "Class ", 406, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 1, 5, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 5, 2, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 1, 4, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 5, 1, 3], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 1, 5, 3], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 1, 5, 2, 4], [1, 1, 1, 1]]} "Class ", 407, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 3, 5, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 3, 2, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 3, 4, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 1, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 3, 5, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 4, 3, 5, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 3, 2, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 3, 4, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 1, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 4, 3, 5, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {1, 2}, {}], [[1, 4, 2, 5, 3], {1, 2}, {}], [[1, 4, 3, 5, 2], {1, 2, 3, 4}, {}], [[2, 4, 3, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 339, 1934, 12627, 92746, 756807, 6794076, 66530866, 705827603, 8063998979, 98711680948, 1288886577289, 17880914118974, 262656716298607, 4072567100045256, 66469814545918262] "" "Class ", 408, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 3, 5, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 1, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 3, 5, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 4, 3, 5, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 1, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 4, 3, 5, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {[1, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 336, 1885, 12039, 86026, 680483, 5899974, 55638763, 566898736, 6205755529, 72632476309, 905053121635, 11962022864202, 167142393896545, 2461715015799172, 38115886238260149] "" "Class ", 409, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 3, 5, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 3, 2, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 3, 4, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 1, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 3, 5, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 1, 3, 2, 4], [0, 1, 0, 0]]} "Class ", 410, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 3, 5, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 3, 2, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 3, 4, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 1, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 3, 5, 1], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 1, 3, 2, 4], [1, 1, 0, 0]]} "Class ", 411, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 3, 5, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 3, 2, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 3, 4, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 1, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 3, 5, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 1, 3, 2, 4], [0, 0, 1, 0]]} "Class ", 412, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 3, 5, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 1, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 3, 5, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 1, 0]]} "Class ", 413, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 3, 5, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 3, 2, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 3, 4, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 1, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 3, 5, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 1, 3, 2, 4], [0, 1, 1, 0]]} "Class ", 414, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 3, 5, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 3, 2, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 3, 4, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 1, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 3, 5, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 1, 3, 2, 4], [1, 1, 1, 0]]} "Class ", 415, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 3, 2, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 3, 4, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 1, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 1, 3, 2, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 3, 2, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 3, 4, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 1, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 1, 3, 2, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 336, 1884, 12020, 85787, 677713, 5868814, 55286167, 562820448, 6157240202, 72036876081, 897509908933, 11863651130263, 165826664226984, 2443777901668815, 37869080501555818] "" "Class ", 416, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 1, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 1, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 333, 1827, 11261, 76557, 568628, 4569807, 39465549, 364014451, 3568188582, 37010384025, 404707476857, 4650395213765, 55992713807090, 704636103919891, 9247119359682701] "" "Class ", 417, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 3, 2, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 3, 4, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 1, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 1, 3, 2, 4], [0, 1, 0, 1]]} "Class ", 418, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 3, 2, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 3, 4, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 1, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 1, 3, 2, 4], [1, 1, 0, 1]]} "Class ", 419, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 3, 5, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 3, 2, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 3, 4, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 1, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 3, 5, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 1, 3, 2, 4], [0, 0, 1, 1]]} "Class ", 420, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 3, 5, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 1, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 3, 5, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 1, 1]]} "Class ", 421, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 3, 5, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 3, 2, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 3, 4, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 1, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 3, 5, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 1, 3, 2, 4], [0, 1, 1, 1]]} "Class ", 422, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 3, 5, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 3, 2, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 3, 4, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 3, 1, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 3, 5, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 1, 3, 2, 4], [1, 1, 1, 1]]} "Class ", 423, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 5, 1, 3], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 5, 1, 2, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 5, 4, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 1, 5, 3], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 5, 1, 3], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[3, 5, 1, 2, 4], [0, 0, 1, 0]]} "Class ", 424, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 5, 1, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 5, 1, 2, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 5, 4, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 1, 5, 3], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 5, 1, 3], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[3, 5, 1, 2, 4], [1, 0, 1, 0]]} "Class ", 425, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 5, 1, 3], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 5, 1, 2, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 5, 4, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 1, 5, 3], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 5, 1, 3], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 5, 1, 2, 4], [0, 1, 1, 0]]} "Class ", 426, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 5, 1, 3], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 5, 1, 2, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 5, 4, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 1, 5, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 5, 1, 3], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 5, 1, 2, 4], [1, 1, 1, 0]]} "Class ", 427, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 5, 1, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 5, 4, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 1, 5, 3], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 5, 1, 3], [1, 0, 0, 0]]} {[[1, 2, 3], [0, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 4, 5, 1, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 5, 4, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 1, 5, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 70, 347, 1996, 13114, 96848, 794123, 7160661, 70406858, 749792121, 8596791249, 105587561672, 1383056108231, 19245536530481, 283521001592794, 4408283007447711, 72141256707303916] "" "Class ", 428, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 5, 1, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 5, 1, 2, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 5, 4, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 1, 5, 3], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 5, 1, 3], [1, 0, 0, 1]]} {[[1, 2, 3], [0, 0]], [[3, 5, 1, 2, 4], [1, 0, 0, 1]]} "Class ", 429, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 5, 1, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 5, 1, 2, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 5, 4, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 1, 5, 3], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 5, 1, 3], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 5, 1, 2, 4], [0, 1, 0, 1]]} "Class ", 430, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 5, 1, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 5, 1, 2, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 5, 4, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 1, 5, 3], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 5, 1, 3], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 5, 1, 2, 4], [1, 1, 0, 1]]} "Class ", 431, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 5, 1, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 5, 1, 2, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 5, 4, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 1, 5, 3], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 5, 1, 3], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[3, 5, 1, 2, 4], [0, 0, 1, 1]]} "Class ", 432, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 5, 1, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 5, 1, 2, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 5, 4, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 1, 5, 3], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 5, 1, 3], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[3, 5, 1, 2, 4], [1, 0, 1, 1]]} "Class ", 433, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 5, 1, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 5, 1, 2, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 5, 4, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 1, 5, 3], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 5, 1, 3], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 5, 1, 2, 4], [0, 1, 1, 1]]} "Class ", 434, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 5, 1, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 5, 1, 2, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 5, 4, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 1, 5, 3], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 5, 1, 3], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 5, 1, 2, 4], [1, 1, 1, 1]]} "Class ", 435, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 5, 3, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 1, 2, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 5, 4, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 1, 3, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 5, 3, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 3, 1, 2, 4], [0, 0, 1, 0]]} "Class ", 436, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 5, 3, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 1, 3, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 5, 3, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 1, 0]]} "Class ", 437, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 5, 3, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 1, 2, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 5, 4, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 1, 3, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 5, 3, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 3, 1, 2, 4], [0, 1, 1, 0]]} "Class ", 438, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 5, 3, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 1, 2, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 5, 4, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 1, 3, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 5, 3, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 3, 1, 2, 4], [1, 1, 1, 0]]} "Class ", 439, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 5, 4, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 1, 3, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 5, 4, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 1, 3, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 70, 347, 1988, 13021, 95551, 778542, 6962858, 67872884, 715800157, 8123087749, 98676929738, 1277741868636, 17567191081306, 255587943030227, 3923070503314205, 63355646413051021] "" "Class ", 440, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 1, 3, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 1, 3, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {2}, {}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {1}, {[0, 0, 0, 1, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 70, 347, 1978, 12823, 92628, 738587, 6430579, 60700330, 616965659, 6716641321, 77944848737, 960319120080, 12516384997238, 172033547213915, 2486555504119551, 37700151189941179] "" "Class ", 441, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 1, 2, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 5, 4, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 1, 3, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 3, 1, 2, 4], [0, 1, 0, 1]]} "Class ", 442, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 1, 2, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 5, 4, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 1, 3, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 3, 1, 2, 4], [1, 1, 0, 1]]} "Class ", 443, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 5, 3, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 1, 2, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 5, 4, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 1, 3, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 5, 3, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 3, 1, 2, 4], [0, 0, 1, 1]]} "Class ", 444, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 5, 3, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 1, 3, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 5, 3, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 1, 1]]} "Class ", 445, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 5, 3, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 1, 2, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 5, 4, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 1, 3, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 5, 3, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 3, 1, 2, 4], [0, 1, 1, 1]]} "Class ", 446, " is:" {{[[1, 2, 3], [0, 0]], [[2, 4, 5, 3, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 1, 2, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 5, 4, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 2, 1, 3, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 4, 5, 3, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 3, 1, 2, 4], [1, 1, 1, 1]]} "Class ", 447, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 1, 4, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 5, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 5, 2, 3], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 1, 4, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 5, 1, 4, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 5, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 5, 2, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 5, 1, 4, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2, 3, 4}, {}], [[3, 5, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 339, 1925, 12532, 91608, 744752, 6657299, 64934507, 686072920, 7806810237, 95176318604, 1237708843622, 17101500999920, 250192845540864, 3863633866168265, 62804933717773669] "" "Class ", 448, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 1, 4, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 5, 1, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 5, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 5, 2, 3], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 1, 4, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 5, 1, 4, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 5, 1, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 5, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 5, 2, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 5, 1, 4, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 337, 1904, 12285, 88990, 715555, 6322990, 60907683, 635199624, 7130208477, 85715284797, 1098676974615, 14957492703312, 215544415863627, 3277751991328300, 52454699298259976] "" "Class ", 449, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 1, 4, 3], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 5, 1, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 5, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 5, 2, 3], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 1, 4, 3], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 2, 5, 1, 4], [0, 1, 0, 0]]} "Class ", 450, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 1, 4, 3], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 5, 1, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 5, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 5, 2, 3], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 1, 4, 3], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 2, 5, 1, 4], [1, 1, 0, 0]]} "Class ", 451, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 1, 4, 3], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 5, 1, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 5, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 5, 2, 3], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 1, 4, 3], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[3, 2, 5, 1, 4], [0, 0, 1, 0]]} "Class ", 452, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 1, 4, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 5, 1, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 5, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 5, 2, 3], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 1, 4, 3], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[3, 2, 5, 1, 4], [1, 0, 1, 0]]} "Class ", 453, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 1, 4, 3], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 5, 1, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 5, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 5, 2, 3], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 1, 4, 3], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 2, 5, 1, 4], [0, 1, 1, 0]]} "Class ", 454, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 1, 4, 3], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 5, 1, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 5, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 5, 2, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 1, 4, 3], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 2, 5, 1, 4], [1, 1, 1, 0]]} "Class ", 455, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 1, 4, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 5, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 5, 2, 3], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 1, 4, 3], [1, 0, 0, 0]]} {[[1, 2, 3], [0, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 5, 1, 4, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 5, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 5, 2, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 337, 1888, 12052, 85892, 677811, 5859284, 55101154, 559852795, 6112936912, 71376970564, 887539463005, 11708892223622, 163347620831840, 2402669473251344, 37162626957565422] "" "Class ", 456, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 1, 4, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 5, 1, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 5, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 5, 2, 3], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 1, 4, 3], [1, 0, 0, 1]]} {[[1, 2, 3], [0, 0]], [[3, 2, 5, 1, 4], [1, 0, 0, 1]]} "Class ", 457, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 1, 4, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 5, 1, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 5, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 5, 2, 3], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 1, 4, 3], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 2, 5, 1, 4], [0, 1, 0, 1]]} "Class ", 458, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 1, 4, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 5, 1, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 5, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 5, 2, 3], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 1, 4, 3], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 2, 5, 1, 4], [1, 1, 0, 1]]} "Class ", 459, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 1, 4, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 5, 1, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 5, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 5, 2, 3], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 1, 4, 3], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[3, 2, 5, 1, 4], [0, 0, 1, 1]]} "Class ", 460, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 1, 4, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 5, 1, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 5, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 5, 2, 3], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 1, 4, 3], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[3, 2, 5, 1, 4], [1, 0, 1, 1]]} "Class ", 461, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 1, 4, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 5, 1, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 5, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 5, 2, 3], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 1, 4, 3], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 2, 5, 1, 4], [0, 1, 1, 1]]} "Class ", 462, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 1, 4, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 5, 1, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 5, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 5, 2, 3], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 1, 4, 3], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 2, 5, 1, 4], [1, 1, 1, 1]]} "Class ", 463, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 3, 1, 4], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 5, 3, 1, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 5, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 5, 2], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 3, 1, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 5, 3, 1, 4], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 5, 3, 1, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 5, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 5, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 5, 3, 1, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 339, 1911, 12342, 89010, 713355, 6265070, 59989253, 620938307, 6916386516, 82429312749, 1047128189169, 14120095430873, 201476710965215, 3032421495421217, 48017232867818666] "" "Class ", 464, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 3, 1, 4], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 5, 3, 1, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 5, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 5, 2], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 3, 1, 4], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[2, 5, 3, 1, 4], [0, 1, 0, 0]]} "Class ", 465, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 3, 1, 4], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 5, 3, 1, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 5, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 5, 2], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 3, 1, 4], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[2, 5, 3, 1, 4], [1, 1, 0, 0]]} "Class ", 466, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 3, 1, 4], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 5, 3, 1, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 5, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 5, 2], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 3, 1, 4], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[2, 5, 3, 1, 4], [1, 0, 1, 0]]} "Class ", 467, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 3, 1, 4], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 5, 3, 1, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 5, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 5, 2], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 3, 1, 4], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[2, 5, 3, 1, 4], [1, 1, 1, 0]]} "Class ", 468, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 3, 1, 4], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 5, 3, 1, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 5, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 5, 2], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 3, 1, 4], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[2, 5, 3, 1, 4], [1, 1, 0, 1]]} "Class ", 469, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 3, 4, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 3, 1, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 3, 5, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 2, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 3, 4, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 5, 3, 4, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 3, 1, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 3, 5, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 2, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 5, 3, 4, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {1, 2}, {}], [[1, 5, 3, 4, 2], {1, 2, 3, 4}, {}], [[2, 5, 3, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 339, 1934, 12627, 92746, 756807, 6794076, 66530866, 705827603, 8063998979, 98711680948, 1288886577289, 17880914118974, 262656716298607, 4072567100045256, 66469814545918262] "" "Class ", 470, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 3, 4, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 2, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 3, 4, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 5, 3, 4, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 2, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 5, 3, 4, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {[1, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 337, 1901, 12230, 88210, 705247, 6189217, 59144878, 611323936, 6795146162, 80826061726, 1024360784250, 13780153221236, 196106599503315, 2943484323306783, 46471832121249056] "" "Class ", 471, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 3, 4, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 3, 1, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 3, 5, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 2, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 3, 4, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 2, 3, 1, 4], [0, 1, 0, 0]]} "Class ", 472, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 3, 4, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 3, 1, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 3, 5, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 2, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 3, 4, 1], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 2, 3, 1, 4], [1, 1, 0, 0]]} "Class ", 473, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 3, 4, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 3, 1, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 3, 5, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 2, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 3, 4, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 2, 3, 1, 4], [0, 0, 1, 0]]} "Class ", 474, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 3, 4, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 2, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 3, 4, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 1, 0]]} "Class ", 475, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 3, 4, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 3, 1, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 3, 5, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 2, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 3, 4, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 2, 3, 1, 4], [0, 1, 1, 0]]} "Class ", 476, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 3, 4, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 3, 1, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 3, 5, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 2, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 3, 4, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 2, 3, 1, 4], [1, 1, 1, 0]]} "Class ", 477, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 3, 1, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 3, 5, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 2, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 2, 3, 1, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 3, 1, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 3, 5, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 2, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 2, 3, 1, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 337, 1897, 12165, 87414, 695678, 6076307, 57766612, 593913998, 6565410325, 77655497059, 978559414808, 13087740217345, 185161251494167, 2762751657400792, 43358231241511066] "" "Class ", 478, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 2, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 2, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {2, 3}, {}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 335, 1863, 11729, 82173, 634120, 5340095, 48719001, 478551419, 5034604972, 56473436809, 672750504197, 8481798552521, 112825728286626, 1579130550013791, 23197459432043001] "" "Class ", 479, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 3, 1, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 3, 5, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 2, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 2, 3, 1, 4], [0, 1, 0, 1]]} "Class ", 480, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 3, 1, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 3, 5, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 2, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 2, 3, 1, 4], [1, 1, 0, 1]]} "Class ", 481, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 3, 4, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 3, 1, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 3, 5, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 2, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 3, 4, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 2, 3, 1, 4], [0, 0, 1, 1]]} "Class ", 482, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 3, 4, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 2, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 3, 4, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 1, 1]]} "Class ", 483, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 3, 4, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 3, 1, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 3, 5, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 2, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 3, 4, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 2, 3, 1, 4], [0, 1, 1, 1]]} "Class ", 484, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 3, 4, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 3, 1, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 3, 5, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 3, 2, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 3, 4, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 2, 3, 1, 4], [1, 1, 1, 1]]} "Class ", 485, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 1, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 5, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 5, 3], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 4, 1, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 1, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 5, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 5, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 5, 4, 1, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {}, {}], [[2, 4, 3, 1, 5], {1, 2, 3}, {}], [[2, 5, 3, 1, 4], {1, 2, 3}, {}], [[2, 5, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 342, 1955, 12859, 94798, 778284, 7019603, 69119497, 736992315, 8464833068, 104153594984, 1367083767861, 19064435442275, 281506536348575, 4387600742525365, 71985689457656733] "" "Class ", 486, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 1, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 5, 2, 1, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 5, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 5, 3], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 4, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 1, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 5, 2, 1, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 5, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 5, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 5, 4, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 339, 1911, 12342, 89010, 713355, 6265070, 59989253, 620938307, 6916386516, 82429312749, 1047128189169, 14120095430873, 201476710965215, 3032421495421217, 48017232867818666] "" "Class ", 487, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 1, 3], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 5, 2, 1, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 5, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 5, 3], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 4, 1, 3], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 5, 2, 1, 4], [0, 1, 0, 0]]} "Class ", 488, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 1, 3], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 5, 2, 1, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 5, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 5, 3], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 4, 1, 3], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 5, 2, 1, 4], [1, 1, 0, 0]]} "Class ", 489, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 1, 3], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 5, 2, 1, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 5, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 5, 3], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 4, 1, 3], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[3, 5, 2, 1, 4], [0, 0, 1, 0]]} "Class ", 490, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 1, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 5, 2, 1, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 5, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 5, 3], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 4, 1, 3], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[3, 5, 2, 1, 4], [1, 0, 1, 0]]} "Class ", 491, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 1, 3], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 5, 2, 1, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 5, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 5, 3], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 4, 1, 3], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 5, 2, 1, 4], [0, 1, 1, 0]]} "Class ", 492, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 1, 3], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 5, 2, 1, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 5, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 5, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 4, 1, 3], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 5, 2, 1, 4], [1, 1, 1, 0]]} "Class ", 493, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 1, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 5, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 5, 3], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 4, 1, 3], [1, 0, 0, 0]]} {[[1, 2, 3], [0, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 1, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 5, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 5, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 340, 1925, 12512, 90944, 735504, 6525808, 63179113, 661759169, 7463517678, 90121134603, 1160450251579, 15869009581439, 229711897781218, 3508762012868799, 56402606105078026] "" "Class ", 494, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 1, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 5, 2, 1, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 5, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 5, 3], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 4, 1, 3], [1, 0, 0, 1]]} {[[1, 2, 3], [0, 0]], [[3, 5, 2, 1, 4], [1, 0, 0, 1]]} "Class ", 495, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 1, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 5, 2, 1, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 5, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 5, 3], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 4, 1, 3], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 5, 2, 1, 4], [0, 1, 0, 1]]} "Class ", 496, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 1, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 5, 2, 1, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 5, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 5, 3], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 4, 1, 3], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 5, 2, 1, 4], [1, 1, 0, 1]]} "Class ", 497, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 1, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 5, 2, 1, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 5, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 5, 3], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 4, 1, 3], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[3, 5, 2, 1, 4], [0, 0, 1, 1]]} "Class ", 498, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 1, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 5, 2, 1, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 5, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 5, 3], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 4, 1, 3], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[3, 5, 2, 1, 4], [1, 0, 1, 1]]} "Class ", 499, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 1, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 5, 2, 1, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 5, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 5, 3], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 4, 1, 3], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 5, 2, 1, 4], [0, 1, 1, 1]]} "Class ", 500, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 1, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 5, 2, 1, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 5, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 5, 3], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 4, 1, 3], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 5, 2, 1, 4], [1, 1, 1, 1]]} "Class ", 501, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 3, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 3, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 4, 3, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 3, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 3, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 5, 4, 3, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 4, 3, 2, 5], {1, 2, 3}, {}], [[1, 5, 3, 2, 4], {1, 2, 3}, {}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {1, 2, 3, 4}, {}], [[2, 5, 4, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 339, 1934, 12627, 92746, 756807, 6794076, 66530866, 705827603, 8063998979, 98711680948, 1288886577289, 17880914118974, 262656716298607, 4072567100045256, 66469814545918262] "" "Class ", 502, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 3, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 3, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 4, 3, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 3, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 3, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 5, 4, 3, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {[1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 335, 1872, 11907, 84683, 666772, 5752426, 53976766, 547108619, 5957554745, 69351154366, 859434211311, 11295896029769, 156946333686850, 2298382353484626, 35382328303205906] "" "Class ", 503, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 3, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 1, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 5, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 3, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 4, 3, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 3, 2, 1, 4], [0, 1, 0, 0]]} "Class ", 504, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 3, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 1, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 5, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 3, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 4, 3, 1], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 3, 2, 1, 4], [1, 1, 0, 0]]} "Class ", 505, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 3, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 5, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 3, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 4, 3, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 1, 0]]} "Class ", 506, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 3, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 3, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 4, 3, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 1, 0]]} "Class ", 507, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 3, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 1, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 5, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 3, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 4, 3, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 3, 2, 1, 4], [0, 1, 1, 0]]} "Class ", 508, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 3, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 1, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 5, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 3, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 4, 3, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 3, 2, 1, 4], [1, 1, 1, 0]]} "Class ", 509, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 337, 1898, 12190, 87777, 700505, 6139344, 58592612, 605073636, 6721110468, 79914731859, 1012682383245, 13624670864655, 193963545011250, 2913001354776351, 46026894832709089] "" "Class ", 510, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {2}, {}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 334, 1846, 11516, 79664, 605206, 5001697, 44654937, 428058397, 4383510889, 47744259518, 551001806097, 6715353876063, 86176147434562, 1161350366516849, 16397190852734079] "" "Class ", 511, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 1, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 5, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 3, 2, 1, 4], [0, 1, 0, 1]]} "Class ", 512, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 1, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 5, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 3, 2, 1, 4], [1, 1, 0, 1]]} "Class ", 513, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 3, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 5, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 3, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 4, 3, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 1, 1]]} "Class ", 514, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 3, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 3, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 4, 3, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 1, 1]]} "Class ", 515, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 3, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 1, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 5, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 3, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 4, 3, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 3, 2, 1, 4], [0, 1, 1, 1]]} "Class ", 516, " is:" {{[[1, 2, 3], [0, 0]], [[2, 5, 4, 3, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 1, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 5, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[4, 1, 2, 3, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[2, 5, 4, 3, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 3, 2, 1, 4], [1, 1, 1, 1]]} "Class ", 517, " is:" {{[[1, 2, 3], [0, 0]], [[3, 1, 4, 5, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 2, 5, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 4, 1, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 2, 1, 4], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 1, 4, 5, 2], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 1, 2, 5, 3], [0, 1, 0, 0]]} "Class ", 518, " is:" {{[[1, 2, 3], [0, 0]], [[3, 1, 4, 5, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 2, 5, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 4, 1, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 2, 1, 4], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 1, 4, 5, 2], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 1, 2, 5, 3], [1, 1, 0, 0]]} "Class ", 519, " is:" {{[[1, 2, 3], [0, 0]], [[3, 1, 4, 5, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 2, 5, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 4, 1, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 2, 1, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 1, 4, 5, 2], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[4, 1, 2, 5, 3], [0, 0, 1, 0]]} "Class ", 520, " is:" {{[[1, 2, 3], [0, 0]], [[3, 1, 4, 5, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 2, 5, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 4, 1, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 2, 1, 4], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 1, 4, 5, 2], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[4, 1, 2, 5, 3], [1, 0, 1, 0]]} "Class ", 521, " is:" {{[[1, 2, 3], [0, 0]], [[3, 1, 4, 5, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 2, 5, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 4, 1, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 2, 1, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 1, 4, 5, 2], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 1, 2, 5, 3], [0, 1, 1, 0]]} "Class ", 522, " is:" {{[[1, 2, 3], [0, 0]], [[3, 1, 4, 5, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 2, 5, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 4, 1, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 2, 1, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 1, 4, 5, 2], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 1, 2, 5, 3], [1, 1, 1, 0]]} "Class ", 523, " is:" {{[[1, 2, 3], [0, 0]], [[3, 1, 4, 5, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 2, 5, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 4, 1, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 2, 1, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 1, 4, 5, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 1, 2, 5, 3], [0, 1, 0, 1]]} "Class ", 524, " is:" {{[[1, 2, 3], [0, 0]], [[3, 1, 4, 5, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 2, 5, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 4, 1, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 2, 1, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 1, 4, 5, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 1, 2, 5, 3], [1, 1, 0, 1]]} "Class ", 525, " is:" {{[[1, 2, 3], [0, 0]], [[3, 1, 4, 5, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 2, 5, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 4, 1, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 2, 1, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 1, 4, 5, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[4, 1, 2, 5, 3], [0, 0, 1, 1]]} "Class ", 526, " is:" {{[[1, 2, 3], [0, 0]], [[3, 1, 4, 5, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 2, 5, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 4, 1, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 2, 1, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 1, 4, 5, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[4, 1, 2, 5, 3], [1, 0, 1, 1]]} "Class ", 527, " is:" {{[[1, 2, 3], [0, 0]], [[3, 1, 4, 5, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 2, 5, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 4, 1, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 2, 1, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 1, 4, 5, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 1, 2, 5, 3], [0, 1, 1, 1]]} "Class ", 528, " is:" {{[[1, 2, 3], [0, 0]], [[3, 1, 4, 5, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 2, 5, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 4, 1, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 2, 1, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 1, 4, 5, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 1, 2, 5, 3], [1, 1, 1, 1]]} "Class ", 529, " is:" {{[[1, 2, 3], [0, 0]], [[3, 1, 5, 4, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 1, 5, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 5, 1, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 1, 5, 4, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 1, 5, 4, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 1, 5, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 5, 1, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[3, 1, 5, 4, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {}], [[2, 1, 4, 3, 5], {1, 2}, {}], [[2, 1, 5, 3, 4], {1, 2, 3}, {}], [[2, 1, 5, 4, 3], {1, 2, 3}, {}], [[3, 1, 5, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 337, 1907, 12358, 90002, 728775, 6489681, 63052543, 663614235, 7521881312, 91346875325, 1183294192833, 16286178598267, 237339473662132, 3650913178394031, 59116620720474639] "" "Class ", 530, " is:" {{[[1, 2, 3], [0, 0]], [[3, 1, 5, 4, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 1, 5, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 5, 1, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 1, 5, 4, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 1, 5, 4, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 1, 5, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 5, 1, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[3, 1, 5, 4, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 333, 1839, 11510, 80215, 617091, 5187862, 47341061, 465827881, 4917084208, 55413970979, 664083530192, 8432297755901, 113087278734254, 1597286662177674, 23699613385737503] "" "Class ", 531, " is:" {{[[1, 2, 3], [0, 0]], [[3, 1, 5, 4, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 1, 5, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 5, 1, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 1, 2, 4], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 1, 5, 4, 2], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 2, 1, 5, 3], [0, 1, 0, 0]]} "Class ", 532, " is:" {{[[1, 2, 3], [0, 0]], [[3, 1, 5, 4, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 1, 5, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 5, 1, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 1, 2, 4], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 1, 5, 4, 2], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 2, 1, 5, 3], [1, 1, 0, 0]]} "Class ", 533, " is:" {{[[1, 2, 3], [0, 0]], [[3, 1, 5, 4, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 1, 5, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 5, 1, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 1, 2, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 1, 5, 4, 2], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[4, 2, 1, 5, 3], [0, 0, 1, 0]]} "Class ", 534, " is:" {{[[1, 2, 3], [0, 0]], [[3, 1, 5, 4, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 1, 5, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 5, 1, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 1, 2, 4], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 1, 5, 4, 2], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[4, 2, 1, 5, 3], [1, 0, 1, 0]]} "Class ", 535, " is:" {{[[1, 2, 3], [0, 0]], [[3, 1, 5, 4, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 1, 5, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 5, 1, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 1, 2, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 1, 5, 4, 2], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 2, 1, 5, 3], [0, 1, 1, 0]]} "Class ", 536, " is:" {{[[1, 2, 3], [0, 0]], [[3, 1, 5, 4, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 1, 5, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 5, 1, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 1, 2, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 1, 5, 4, 2], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 2, 1, 5, 3], [1, 1, 1, 0]]} "Class ", 537, " is:" {{[[1, 2, 3], [0, 0]], [[3, 1, 5, 4, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 1, 5, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 5, 1, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 1, 2, 4], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 1, 5, 4, 2], [1, 0, 0, 0]]} {[[1, 2, 3], [0, 0]], [[4, 2, 1, 5, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 1, 5, 4, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 1, 5, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 5, 1, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 1, 2, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[4, 2, 1, 5, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {[0, 0, 1, 0, 0]}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 334, 1859, 11769, 83262, 652113, 5595466, 52225186, 526571546, 5704578932, 66073890872, 814838311569, 10659043109315, 147416824189308, 2149178828888961, 32941773664073309] "" "Class ", 538, " is:" {{[[1, 2, 3], [0, 0]], [[3, 1, 5, 4, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 1, 5, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 5, 1, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 1, 2, 4], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 1, 5, 4, 2], [1, 0, 0, 1]]} {[[1, 2, 3], [0, 0]], [[4, 2, 1, 5, 3], [1, 0, 0, 1]]} "Class ", 539, " is:" {{[[1, 2, 3], [0, 0]], [[3, 1, 5, 4, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 1, 5, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 5, 1, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 1, 2, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 1, 5, 4, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 2, 1, 5, 3], [0, 1, 0, 1]]} "Class ", 540, " is:" {{[[1, 2, 3], [0, 0]], [[3, 1, 5, 4, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 1, 5, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 5, 1, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 1, 2, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 1, 5, 4, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 2, 1, 5, 3], [1, 1, 0, 1]]} "Class ", 541, " is:" {{[[1, 2, 3], [0, 0]], [[3, 1, 5, 4, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 1, 5, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 5, 1, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 1, 2, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 1, 5, 4, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[4, 2, 1, 5, 3], [0, 0, 1, 1]]} "Class ", 542, " is:" {{[[1, 2, 3], [0, 0]], [[3, 1, 5, 4, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 1, 5, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 5, 1, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 1, 2, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 1, 5, 4, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[4, 2, 1, 5, 3], [1, 0, 1, 1]]} "Class ", 543, " is:" {{[[1, 2, 3], [0, 0]], [[3, 1, 5, 4, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 1, 5, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 5, 1, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 1, 2, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 1, 5, 4, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 2, 1, 5, 3], [0, 1, 1, 1]]} "Class ", 544, " is:" {{[[1, 2, 3], [0, 0]], [[3, 1, 5, 4, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 1, 5, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 5, 1, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 5, 1, 2, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 1, 5, 4, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 2, 1, 5, 3], [1, 1, 1, 1]]} "Class ", 545, " is:" {{[[1, 2, 3], [0, 0]], [[3, 2, 4, 5, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 2, 4, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 4, 2, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 2, 1, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 2, 4, 5, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 1, 2, 4, 3], [0, 1, 0, 0]]} "Class ", 546, " is:" {{[[1, 2, 3], [0, 0]], [[3, 2, 4, 5, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 2, 4, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 4, 2, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 2, 1, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 2, 4, 5, 1], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 1, 2, 4, 3], [1, 1, 0, 0]]} "Class ", 547, " is:" {{[[1, 2, 3], [0, 0]], [[3, 2, 4, 5, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 2, 4, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 4, 2, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 2, 1, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 2, 4, 5, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 1, 2, 4, 3], [0, 0, 1, 0]]} "Class ", 548, " is:" {{[[1, 2, 3], [0, 0]], [[3, 2, 4, 5, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 2, 1, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 2, 4, 5, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 1, 0]]} "Class ", 549, " is:" {{[[1, 2, 3], [0, 0]], [[3, 2, 4, 5, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 2, 4, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 4, 2, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 2, 1, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 2, 4, 5, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 1, 2, 4, 3], [0, 1, 1, 0]]} "Class ", 550, " is:" {{[[1, 2, 3], [0, 0]], [[3, 2, 4, 5, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 2, 4, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 4, 2, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 2, 1, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 2, 4, 5, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 1, 2, 4, 3], [1, 1, 1, 0]]} "Class ", 551, " is:" {{[[1, 2, 3], [0, 0]], [[3, 2, 4, 5, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 2, 4, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 4, 2, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 2, 1, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 2, 4, 5, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 1, 2, 4, 3], [0, 1, 0, 1]]} "Class ", 552, " is:" {{[[1, 2, 3], [0, 0]], [[3, 2, 4, 5, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 2, 4, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 4, 2, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 2, 1, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 2, 4, 5, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 1, 2, 4, 3], [1, 1, 0, 1]]} "Class ", 553, " is:" {{[[1, 2, 3], [0, 0]], [[3, 2, 4, 5, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 2, 4, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 4, 2, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 2, 1, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 2, 4, 5, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 1, 2, 4, 3], [0, 0, 1, 1]]} "Class ", 554, " is:" {{[[1, 2, 3], [0, 0]], [[3, 2, 4, 5, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 2, 1, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 2, 4, 5, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 1, 1]]} "Class ", 555, " is:" {{[[1, 2, 3], [0, 0]], [[3, 2, 4, 5, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 2, 4, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 4, 2, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 2, 1, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 2, 4, 5, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 1, 2, 4, 3], [0, 1, 1, 1]]} "Class ", 556, " is:" {{[[1, 2, 3], [0, 0]], [[3, 2, 4, 5, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 2, 4, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 4, 2, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 2, 1, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 2, 4, 5, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 1, 2, 4, 3], [1, 1, 1, 1]]} "Class ", 557, " is:" {{[[1, 2, 3], [0, 0]], [[3, 2, 5, 4, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 1, 4, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 5, 2, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 2, 5, 4, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 2, 5, 4, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 1, 4, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 5, 2, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[3, 2, 5, 4, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {}], [[2, 1, 4, 3, 5], {1, 2}, {}], [[2, 1, 5, 3, 4], {1, 2, 3}, {}], [[2, 1, 5, 4, 3], {1, 2, 3}, {}], [[3, 1, 5, 4, 2], {1, 2, 3}, {}], [[3, 2, 5, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 337, 1912, 12420, 90683, 736046, 6570389, 63990019, 675109927, 7670649468, 93378723743, 1212536775650, 16728987051331, 244381616523424, 3768323985521521, 61165209457069496] "" "Class ", 558, " is:" {{[[1, 2, 3], [0, 0]], [[3, 2, 5, 4, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 2, 5, 4, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 2, 5, 4, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[3, 2, 5, 4, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {[1, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 333, 1840, 11530, 80490, 620506, 5229036, 47840888, 472035088, 4996692480, 56473183658, 678741056378, 8643455608344, 116254762402680, 1646744603698600, 24502961404471640] "" "Class ", 559, " is:" {{[[1, 2, 3], [0, 0]], [[3, 2, 5, 4, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 1, 4, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 5, 2, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 2, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 2, 5, 4, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 2, 1, 4, 3], [0, 1, 0, 0]]} "Class ", 560, " is:" {{[[1, 2, 3], [0, 0]], [[3, 2, 5, 4, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 1, 4, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 5, 2, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 2, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 2, 5, 4, 1], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 2, 1, 4, 3], [1, 1, 0, 0]]} "Class ", 561, " is:" {{[[1, 2, 3], [0, 0]], [[3, 2, 5, 4, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 1, 4, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 5, 2, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 2, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 2, 5, 4, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 2, 1, 4, 3], [0, 0, 1, 0]]} "Class ", 562, " is:" {{[[1, 2, 3], [0, 0]], [[3, 2, 5, 4, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 2, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 2, 5, 4, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 1, 0]]} "Class ", 563, " is:" {{[[1, 2, 3], [0, 0]], [[3, 2, 5, 4, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 1, 4, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 5, 2, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 2, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 2, 5, 4, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 2, 1, 4, 3], [0, 1, 1, 0]]} "Class ", 564, " is:" {{[[1, 2, 3], [0, 0]], [[3, 2, 5, 4, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 1, 4, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 5, 2, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 2, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 2, 5, 4, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 2, 1, 4, 3], [1, 1, 1, 0]]} "Class ", 565, " is:" {{[[1, 2, 3], [0, 0]], [[3, 2, 5, 4, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 1, 4, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 5, 2, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 2, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 2, 5, 4, 1], [1, 0, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 2, 1, 4, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 2, 5, 4, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 1, 4, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 5, 2, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 2, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 2, 1, 4, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {[0, 0, 1, 0, 0]}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 335, 1883, 12090, 87018, 695123, 6095283, 58245878, 602147762, 6697947801, 79748074329, 1012068359114, 13636690299177, 194432955141290, 2924557887863840, 46281742755768579] "" "Class ", 566, " is:" {{[[1, 2, 3], [0, 0]], [[3, 2, 5, 4, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 2, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 2, 5, 4, 1], [1, 0, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 2, 5, 4, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 2, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {2}, {}], [[4, 2, 1, 3], {2}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 331, 1801, 10997, 73963, 543487, 4318053, 36867583, 336044689, 3254808582, 33346503799, 360097011673, 4084869252349, 48541171804646, 602694107952480, 7801271810693335] "" "Class ", 567, " is:" {{[[1, 2, 3], [0, 0]], [[3, 2, 5, 4, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 1, 4, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 5, 2, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 2, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 2, 5, 4, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 2, 1, 4, 3], [0, 1, 0, 1]]} "Class ", 568, " is:" {{[[1, 2, 3], [0, 0]], [[3, 2, 5, 4, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 1, 4, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 5, 2, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 2, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 2, 5, 4, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 2, 1, 4, 3], [1, 1, 0, 1]]} "Class ", 569, " is:" {{[[1, 2, 3], [0, 0]], [[3, 2, 5, 4, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 1, 4, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 5, 2, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 2, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 2, 5, 4, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 2, 1, 4, 3], [0, 0, 1, 1]]} "Class ", 570, " is:" {{[[1, 2, 3], [0, 0]], [[3, 2, 5, 4, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 2, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 2, 5, 4, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 1, 1]]} "Class ", 571, " is:" {{[[1, 2, 3], [0, 0]], [[3, 2, 5, 4, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 1, 4, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 5, 2, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 2, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 2, 5, 4, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 2, 1, 4, 3], [0, 1, 1, 1]]} "Class ", 572, " is:" {{[[1, 2, 3], [0, 0]], [[3, 2, 5, 4, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 1, 4, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 5, 2, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 4, 1, 2, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 2, 5, 4, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 2, 1, 4, 3], [1, 1, 1, 1]]} "Class ", 573, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 1, 5, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 5, 2, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 1, 4, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 1, 5, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 4, 1, 5, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 5, 2, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 1, 4, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[3, 4, 1, 5, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4}, {}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 340, 1943, 12725, 93683, 766623, 6899757, 67747834, 720624976, 8254902990, 101315582213, 1326386191489, 18449829379372, 271730527296421, 4224404993124360, 69130401761709126] "" "Class ", 574, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 1, 5, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 5, 2, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 1, 4, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 1, 5, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 4, 1, 5, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 5, 2, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 1, 4, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[3, 4, 1, 5, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 337, 1901, 12232, 88252, 705864, 6197488, 59252463, 612736563, 6814165555, 81091082980, 1028199561916, 13838074129948, 197017612130696, 2958420057560486, 46726934609544589] "" "Class ", 575, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 1, 5, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 5, 2, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 1, 4, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 5, 1, 4], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 1, 5, 2], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 1, 5, 2, 3], [0, 1, 0, 0]]} "Class ", 576, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 1, 5, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 5, 2, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 1, 4, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 5, 1, 4], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 1, 5, 2], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 1, 5, 2, 3], [1, 1, 0, 0]]} "Class ", 577, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 1, 5, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 5, 2, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 1, 4, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 5, 1, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 1, 5, 2], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[4, 1, 5, 2, 3], [0, 0, 1, 0]]} "Class ", 578, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 1, 5, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 5, 2, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 1, 4, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 5, 1, 4], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 1, 5, 2], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[4, 1, 5, 2, 3], [1, 0, 1, 0]]} "Class ", 579, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 1, 5, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 5, 2, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 1, 4, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 5, 1, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 1, 5, 2], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 1, 5, 2, 3], [0, 1, 1, 0]]} "Class ", 580, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 1, 5, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 5, 2, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 1, 4, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 5, 1, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 1, 5, 2], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 1, 5, 2, 3], [1, 1, 1, 0]]} "Class ", 581, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 1, 5, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 5, 2, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 1, 4, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 5, 1, 4], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 1, 5, 2], [1, 0, 0, 0]]} {[[1, 2, 3], [0, 0]], [[4, 1, 5, 2, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 4, 1, 5, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 5, 2, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 1, 4, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 5, 1, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[4, 1, 5, 2, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 336, 1881, 11989, 85385, 673196, 5814884, 54632370, 554517963, 6047453438, 70517216945, 875522764236, 11531044481118, 160572155156169, 2357164955701094, 36381239131978358] "" "Class ", 582, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 1, 5, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 5, 2, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 1, 4, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 5, 1, 4], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 1, 5, 2], [1, 0, 0, 1]]} {[[1, 2, 3], [0, 0]], [[4, 1, 5, 2, 3], [1, 0, 0, 1]]} "Class ", 583, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 1, 5, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 5, 2, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 1, 4, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 5, 1, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 1, 5, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 1, 5, 2, 3], [0, 1, 0, 1]]} "Class ", 584, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 1, 5, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 5, 2, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 1, 4, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 5, 1, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 1, 5, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 1, 5, 2, 3], [1, 1, 0, 1]]} "Class ", 585, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 1, 5, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 5, 2, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 1, 4, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 5, 1, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 1, 5, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[4, 1, 5, 2, 3], [0, 0, 1, 1]]} "Class ", 586, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 1, 5, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 5, 2, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 1, 4, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 5, 1, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 1, 5, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[4, 1, 5, 2, 3], [1, 0, 1, 1]]} "Class ", 587, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 1, 5, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 5, 2, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 1, 4, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 5, 1, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 1, 5, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 1, 5, 2, 3], [0, 1, 1, 1]]} "Class ", 588, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 1, 5, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 5, 2, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 1, 4, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 5, 1, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 1, 5, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 1, 5, 2, 3], [1, 1, 1, 1]]} "Class ", 589, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 2, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 4, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 2, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 4, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4}, {}], [[3, 4, 1, 5, 2], {1, 2, 3, 4}, {}], [[3, 4, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 340, 1949, 12780, 94269, 772431, 6963517, 68475331, 729508045, 8369447784, 102880403203, 1348947461191, 18792605962333, 277205899706725, 4316174184902835, 70741119536657170] "" "Class ", 590, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 337, 1902, 12247, 88429, 707905, 6220903, 59531111, 616184676, 6858852118, 81697963741, 1036839422953, 13966927737153, 199028679651193, 2991227659516787, 47285625659155583] "" "Class ", 591, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 2, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 4, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 1, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 1, 4, 2, 3], [0, 1, 0, 0]]} "Class ", 592, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 2, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 4, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 1, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 1, 4, 2, 3], [1, 1, 0, 0]]} "Class ", 593, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 2, 5, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 2, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 4, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 1, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 2, 5, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 1, 4, 2, 3], [0, 0, 1, 0]]} "Class ", 594, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 2, 5, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 1, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 2, 5, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 1, 0]]} "Class ", 595, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 2, 5, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 2, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 4, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 1, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 2, 5, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 1, 4, 2, 3], [0, 1, 1, 0]]} "Class ", 596, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 2, 5, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 2, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 4, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 1, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 2, 5, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 1, 4, 2, 3], [1, 1, 1, 0]]} "Class ", 597, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 2, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 4, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 1, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 1, 4, 2, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 2, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 4, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 1, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 1, 4, 2, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 336, 1885, 12037, 85995, 680174, 5897480, 55629004, 567060181, 6211877888, 72772245155, 907858602986, 12015917154609, 168167769516726, 2481357174792973, 38498187533419373] "" "Class ", 598, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 1, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 1, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {2, 3}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 333, 1827, 11261, 76557, 568628, 4569807, 39465549, 364014451, 3568188582, 37010384025, 404707476857, 4650395213765, 55992713807090, 704636103919891, 9247119359682701] "" "Class ", 599, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 2, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 4, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 1, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 1, 4, 2, 3], [0, 1, 0, 1]]} "Class ", 600, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 2, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 4, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 1, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 1, 4, 2, 3], [1, 1, 0, 1]]} "Class ", 601, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 2, 5, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 2, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 4, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 1, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 2, 5, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 1, 4, 2, 3], [0, 0, 1, 1]]} "Class ", 602, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 2, 5, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 1, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 2, 5, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 1, 1]]} "Class ", 603, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 2, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 4, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 1, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 1, 4, 2, 3], [0, 1, 1, 1]]} "Class ", 604, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 2, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 4, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 4, 1, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 1, 4, 2, 3], [1, 1, 1, 1]]} "Class ", 605, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 5, 1, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 1, 2, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 5, 4, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 1, 5, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 5, 1, 2], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[4, 5, 1, 2, 3], [0, 0, 1, 0]]} "Class ", 606, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 5, 1, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 1, 2, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 5, 4, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 1, 5, 4], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 5, 1, 2], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[4, 5, 1, 2, 3], [1, 0, 1, 0]]} "Class ", 607, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 5, 1, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 1, 5, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 5, 1, 2], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 1, 0]]} "Class ", 608, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 5, 1, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 1, 2, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 5, 4, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 1, 5, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 5, 1, 2], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 5, 1, 2, 3], [1, 1, 1, 0]]} "Class ", 609, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 5, 4, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 1, 5, 4], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 0, 0]]} {[[1, 2, 3], [0, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 5, 4, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 1, 5, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 70, 347, 1998, 13145, 97244, 798845, 7217234, 71101641, 758666487, 8715177875, 107242223670, 1407292940311, 19617556732845, 289499448351417, 4508763786242665, 73905272995100297] "" "Class ", 610, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 1, 2, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 5, 4, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 1, 5, 4], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 0, 1]]} {[[1, 2, 3], [0, 0]], [[4, 5, 1, 2, 3], [1, 0, 0, 1]]} "Class ", 611, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 1, 5, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 1, 5, 4], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {2, 3}, {}], [[2, 4, 1, 3], {2, 3}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {}, {[0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {3, 4}, {[0, 0, 0, 1, 0, 0]}], [[4, 5, 2, 3, 1], {3, 4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 70, 347, 1989, 13000, 95159, 771581, 6859088, 66324077, 692790525, 7772409074, 93187522761, 1188843617181, 16076852753078, 229680685594351, 3456154428478073, 54631268653726040] "" "Class ", 612, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 1, 2, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 5, 4, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 1, 5, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 5, 1, 2, 3], [1, 1, 0, 1]]} "Class ", 613, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 5, 1, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 1, 2, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 5, 4, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 1, 5, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 5, 1, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[4, 5, 1, 2, 3], [0, 0, 1, 1]]} "Class ", 614, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 5, 1, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 1, 2, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 5, 4, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 1, 5, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 5, 1, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[4, 5, 1, 2, 3], [1, 0, 1, 1]]} "Class ", 615, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 5, 1, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 1, 5, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 5, 1, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]} "Class ", 616, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 5, 1, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 1, 2, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 5, 4, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 1, 5, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 5, 1, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 5, 1, 2, 3], [1, 1, 1, 1]]} "Class ", 617, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 5, 2, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 1, 2, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 5, 4, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 1, 4, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 5, 2, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 4, 1, 2, 3], [0, 0, 1, 0]]} "Class ", 618, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 5, 2, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 1, 4, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 5, 2, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 1, 0]]} "Class ", 619, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 5, 2, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 1, 4, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 5, 2, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 0]]} "Class ", 620, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 5, 2, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 1, 4, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 5, 2, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]} "Class ", 621, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 5, 4, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 5, 4, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {[0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 70, 347, 1988, 13021, 95551, 778542, 6962858, 67872884, 715800157, 8123087749, 98676929738, 1277741868636, 17567191081306, 255587943030227, 3923070503314205, 63355646413051021] "" "Class ", 622, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {2}, {}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {[0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 70, 347, 1978, 12825, 92637, 738550, 6428861, 60660611, 616298266, 6705688721, 77770997093, 957529574711, 12470987246656, 171276983855257, 2473611630575551, 37472212173504039] "" "Class ", 623, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 1, 4], {3}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 1, 3], {3}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {[0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 3}, {[0, 0, 0, 1, 0, 0]}], [[5, 4, 2, 3, 1], {1, 3}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 70, 347, 1979, 12830, 92609, 737257, 6400736, 60179441, 608433373, 6580551314, 75766839249, 925000807137, 11931196763286, 162091933625903, 2312910812790767, 34578210067677842] "" "Class ", 624, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 1, 4], {3}, {}], [[3, 2, 4, 1], {}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {2}, {}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {[0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [[3, 2, 4, 1, 5], {3, 4}, {}], [[3, 2, 5, 1, 4], {1, 2}, {}], [[4, 2, 5, 1, 3], {1, 2}, {}], [[4, 3, 5, 1, 2], {1, 2}, {[0, 0, 1, 0, 0, 0]}], [[4, 3, 5, 2, 1], {4}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 70, 347, 1971, 12660, 89957, 699721, 5890978, 53277357, 514046693, 5262918138, 56908416889, 647349964301, 7720091741958, 96234355291879, 1250603220382679, 16903576303492572] "" "Class ", 625, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 5, 2, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 1, 2, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 5, 4, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 1, 4, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 5, 2, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 4, 1, 2, 3], [0, 0, 1, 1]]} "Class ", 626, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 5, 2, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 1, 4, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 5, 2, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 1, 1]]} "Class ", 627, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 5, 2, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 1, 4, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 5, 2, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]} "Class ", 628, " is:" {{[[1, 2, 3], [0, 0]], [[3, 4, 5, 2, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 4, 5, 2, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]} "Class ", 629, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 1, 4, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 5, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 5, 2, 4], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 1, 4, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 5, 1, 4, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 5, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 5, 2, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[3, 5, 1, 4, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2, 3, 4}, {}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 340, 1943, 12725, 93683, 766623, 6899757, 67747834, 720624976, 8254902990, 101315582213, 1326386191489, 18449829379372, 271730527296421, 4224404993124360, 69130401761709126] "" "Class ", 630, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 1, 4, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 5, 1, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 5, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 5, 2, 4], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 1, 4, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 5, 1, 4, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 5, 1, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 5, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 5, 2, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[3, 5, 1, 4, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 338, 1918, 12435, 90539, 731572, 6495518, 62854581, 658367560, 7421080907, 89567443245, 1152427298373, 15746469900065, 227706982323095, 3474317407484189, 55779492945551438] "" "Class ", 631, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 1, 4, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 5, 1, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 5, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 5, 2, 4], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 1, 4, 2], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 2, 5, 1, 3], [0, 1, 0, 0]]} "Class ", 632, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 1, 4, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 5, 1, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 5, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 5, 2, 4], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 1, 4, 2], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 2, 5, 1, 3], [1, 1, 0, 0]]} "Class ", 633, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 1, 4, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 5, 1, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 5, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 5, 2, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 1, 4, 2], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[4, 2, 5, 1, 3], [0, 0, 1, 0]]} "Class ", 634, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 1, 4, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 5, 1, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 5, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 5, 2, 4], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 1, 4, 2], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[4, 2, 5, 1, 3], [1, 0, 1, 0]]} "Class ", 635, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 1, 4, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 5, 1, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 5, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 5, 2, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 1, 4, 2], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 2, 5, 1, 3], [0, 1, 1, 0]]} "Class ", 636, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 1, 4, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 5, 1, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 5, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 5, 2, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 1, 4, 2], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 2, 5, 1, 3], [1, 1, 1, 0]]} "Class ", 637, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 1, 4, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 5, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 5, 2, 4], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 1, 4, 2], [1, 0, 0, 0]]} {[[1, 2, 3], [0, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 5, 1, 4, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 5, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 5, 2, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 337, 1893, 12114, 86668, 686488, 5959170, 56270000, 574114493, 6294221184, 73789445280, 921135309881, 12198614069325, 170812878997780, 2521567123997607, 39138741125837486] "" "Class ", 638, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 1, 4, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 5, 1, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 5, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 5, 2, 4], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 1, 4, 2], [1, 0, 0, 1]]} {[[1, 2, 3], [0, 0]], [[4, 2, 5, 1, 3], [1, 0, 0, 1]]} "Class ", 639, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 1, 4, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 5, 1, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 5, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 5, 2, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 1, 4, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 2, 5, 1, 3], [0, 1, 0, 1]]} "Class ", 640, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 1, 4, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 5, 1, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 5, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 5, 2, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 1, 4, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 2, 5, 1, 3], [1, 1, 0, 1]]} "Class ", 641, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 1, 4, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 5, 1, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 5, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 5, 2, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 1, 4, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[4, 2, 5, 1, 3], [0, 0, 1, 1]]} "Class ", 642, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 1, 4, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 5, 1, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 5, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 5, 2, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 1, 4, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[4, 2, 5, 1, 3], [1, 0, 1, 1]]} "Class ", 643, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 1, 4, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 5, 1, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 5, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 5, 2, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 1, 4, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 2, 5, 1, 3], [0, 1, 1, 1]]} "Class ", 644, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 1, 4, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 2, 5, 1, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 5, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 5, 2, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 1, 4, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 2, 5, 1, 3], [1, 1, 1, 1]]} "Class ", 645, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 5, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 2, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 5, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 2, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2, 3, 4}, {}], [[3, 5, 1, 4, 2], {1, 2, 3, 4}, {}], [[3, 5, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 340, 1950, 12791, 94363, 773398, 6973637, 68591405, 730902357, 8387355078, 103123492602, 1352438907443, 18845470263140, 278048042934595, 4330257923031453, 70987866483366073] "" "Class ", 646, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 2, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 2, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {[1, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 338, 1919, 12448, 90675, 733041, 6511564, 63039878, 660612174, 7449762133, 89953429409, 1157893474042, 15827816779857, 228977050794555, 3495087943487876, 56134706426534891] "" "Class ", 647, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 4, 1, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 5, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 2, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 2, 4, 1, 3], [0, 1, 0, 0]]} "Class ", 648, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 4, 1, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 5, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 2, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 2, 4, 1, 3], [1, 1, 0, 0]]} "Class ", 649, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 2, 4, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 5, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 2, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 2, 4, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 1, 0]]} "Class ", 650, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 2, 4, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 2, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 2, 4, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 1, 0]]} "Class ", 651, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 2, 4, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 4, 1, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 5, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 2, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 2, 4, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 2, 4, 1, 3], [0, 1, 1, 0]]} "Class ", 652, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 2, 4, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 4, 1, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 5, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 2, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 2, 4, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 2, 4, 1, 3], [1, 1, 1, 0]]} "Class ", 653, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 5, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 2, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 5, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 2, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 337, 1899, 12194, 87735, 699278, 6116003, 58225695, 599426492, 6634934784, 78575549957, 991340247019, 13273990849082, 188004845883576, 2808181659350787, 44116620367147863] "" "Class ", 654, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 2, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 2, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {2, 3}, {}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 335, 1863, 11729, 82173, 634120, 5340095, 48719001, 478551419, 5034604972, 56473436809, 672750504197, 8481798552521, 112825728286626, 1579130550013791, 23197459432043001] "" "Class ", 655, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 4, 1, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 5, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 2, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 2, 4, 1, 3], [0, 1, 0, 1]]} "Class ", 656, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 4, 1, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 5, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 2, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 2, 4, 1, 3], [1, 1, 0, 1]]} "Class ", 657, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 2, 4, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 5, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 2, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 2, 4, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 1, 1]]} "Class ", 658, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 2, 4, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 2, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 2, 4, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 1, 1]]} "Class ", 659, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 2, 4, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 4, 1, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 5, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 2, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 2, 4, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 2, 4, 1, 3], [0, 1, 1, 1]]} "Class ", 660, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 2, 4, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 4, 1, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 5, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 4, 2, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 2, 4, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 2, 4, 1, 3], [1, 1, 1, 1]]} "Class ", 661, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 5, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 5, 4], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 5, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 5, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {}, {}], [[2, 4, 3, 1, 5], {1, 2, 3}, {}], [[2, 5, 3, 1, 4], {1, 2, 3}, {}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 4, 2, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 344, 1976, 13065, 96797, 798563, 7237848, 71614208, 767328635, 8856117336, 109500268334, 1444260640067, 20238958316028, 300305790542483, 4703434350915986, 77543574121444869] "" "Class ", 662, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 2, 1, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 5, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 5, 4], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 2, 1, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 5, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 5, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 340, 1924, 12485, 90508, 729194, 6438552, 61972308, 644768538, 7217405498, 86431888479, 1103063460087, 14941145247128, 214112870370188, 3236067545346069, 51448164919568396] "" "Class ", 663, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 5, 4], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 5, 4], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {2, 3}, {}], [[2, 4, 1, 3], {2, 3}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {}, {}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 1, 5], {2, 3, 4}, {}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {2, 3, 4}, {}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3}, {}], [[4, 5, 3, 1, 2], {3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 339, 1923, 12505, 91183, 738835, 6573941, 63763247, 669195617, 7556711649, 91336934397, 1176551389545, 16088928346285, 232764069722665, 3551780464309279, 57007331951694761] "" "Class ", 664, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 2, 1, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 5, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 5, 4], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 5, 2, 1, 3], [1, 1, 0, 0]]} "Class ", 665, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 2, 1, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 5, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 5, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[4, 5, 2, 1, 3], [0, 0, 1, 0]]} "Class ", 666, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 2, 1, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 5, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 5, 4], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[4, 5, 2, 1, 3], [1, 0, 1, 0]]} "Class ", 667, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 5, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 1, 0]]} "Class ", 668, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 2, 1, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 5, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 5, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 5, 2, 1, 3], [1, 1, 1, 0]]} "Class ", 669, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 5, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 5, 4], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 0, 0]]} {[[1, 2, 3], [0, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 5, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 5, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 341, 1938, 12654, 92442, 751406, 6701561, 65206799, 686403051, 7778553335, 94364771277, 1220562308170, 16763933711709, 243687362762228, 3737395424717043, 60314066601517362] "" "Class ", 670, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 2, 1, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 5, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 5, 4], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 0, 1]]} {[[1, 2, 3], [0, 0]], [[4, 5, 2, 1, 3], [1, 0, 0, 1]]} "Class ", 671, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 5, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 5, 4], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {2, 3}, {}], [[2, 4, 1, 3], {2, 3}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {3, 4}, {[0, 0, 0, 1, 0, 0]}], [[4, 5, 2, 3, 1], {3, 4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 337, 1885, 12005, 85139, 667277, 5710755, 53018057, 529988557, 5674875963, 64755330705, 784265198477, 10043547039683, 135570473047475, 1923260314604767, 28602235393647965] "" "Class ", 672, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 2, 1, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 5, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 5, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 5, 2, 1, 3], [1, 1, 0, 1]]} "Class ", 673, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 2, 1, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 5, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 5, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[4, 5, 2, 1, 3], [0, 0, 1, 1]]} "Class ", 674, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 2, 1, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 5, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 5, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[4, 5, 2, 1, 3], [1, 0, 1, 1]]} "Class ", 675, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 5, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]} "Class ", 676, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 2, 1, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 5, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 5, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 4, 1, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 5, 2, 1, 3], [1, 1, 1, 1]]} "Class ", 677, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {}, {}], [[2, 4, 3, 1, 5], {1, 2, 3}, {}], [[2, 5, 3, 1, 4], {1, 2, 3}, {}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 340, 1948, 12768, 94154, 771206, 6950373, 68322232, 727643278, 8345255439, 102549324806, 1344160973660, 18719737217154, 276039761403556, 4296596059539859, 70396965736734762] "" "Class ", 678, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 336, 1895, 12213, 88257, 707714, 6229305, 59741775, 619793468, 6917456220, 82630236336, 1051920565844, 14216398491945, 203285655658188, 3066264732745631, 48654982134416271] "" "Class ", 679, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 1, 4], {3}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 1, 3], {3}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {}, {}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 1, 5], {3, 4}, {}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {3, 4}, {}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {3}, {}], [[5, 4, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {3}, {}], [[5, 4, 3, 1, 2], {3}, {}], [[5, 4, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 335, 1874, 11943, 85157, 672281, 5815431, 54698528, 555610841, 6060706656, 70648426733, 876318805100, 11523377142984, 160109454929702, 2343653093827790, 36046058064901140] "" "Class ", 680, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 5, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [1, 1, 0, 0]]} "Class ", 681, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 5, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 4, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 1, 0]]} "Class ", 682, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 4, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 1, 0]]} "Class ", 683, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 4, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 1, 0]]} "Class ", 684, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 5, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 4, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [1, 1, 1, 0]]} "Class ", 685, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 337, 1898, 12190, 87777, 700505, 6139344, 58592612, 605073636, 6721110468, 79914731859, 1012682383245, 13624670864655, 193963545011250, 2913001354776351, 46026894832709089] "" "Class ", 686, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {2}, {}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 333, 1832, 11364, 78074, 588840, 4828027, 42757825, 406453498, 4127445339, 44575155416, 510107674432, 6164923370593, 78458941347828, 1048711817118728, 14687881278036814] "" "Class ", 687, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 1, 4], {3}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 1, 3], {3}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {1}, {[0, 0, 1, 0, 0]}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 3}, {[0, 0, 0, 1, 0, 0]}], [[5, 4, 2, 3, 1], {1, 3}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 333, 1828, 11279, 76827, 572164, 4615131, 40039641, 371393201, 3664740378, 38306937209, 422594552957, 4904543878455, 59712160243080, 760734154998235, 10118771169046489] "" "Class ", 688, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]} "Class ", 689, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 5, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 4, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 1, 1]]} "Class ", 690, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 4, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 1, 1]]} "Class ", 691, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 4, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 1, 1]]} "Class ", 692, " is:" {{[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 5, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[3, 1, 2, 4, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[3, 5, 4, 2, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 4, 2, 1, 3], [1, 1, 1, 1]]} "Class ", 693, " is:" {{[[1, 2, 3], [0, 0]], [[4, 1, 3, 5, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 3, 5, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 3, 1, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 3, 1, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 1, 3, 5, 2], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 1, 3, 5, 2], [0, 1, 0, 0]]} "Class ", 694, " is:" {{[[1, 2, 3], [0, 0]], [[4, 1, 3, 5, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 3, 5, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 3, 1, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 3, 1, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 1, 3, 5, 2], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 1, 3, 5, 2], [1, 1, 0, 0]]} "Class ", 695, " is:" {{[[1, 2, 3], [0, 0]], [[4, 1, 3, 5, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 3, 5, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 3, 1, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 3, 1, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 1, 3, 5, 2], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[4, 1, 3, 5, 2], [1, 0, 1, 0]]} "Class ", 696, " is:" {{[[1, 2, 3], [0, 0]], [[4, 1, 3, 5, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 3, 5, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 3, 1, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 3, 1, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 1, 3, 5, 2], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 1, 3, 5, 2], [1, 1, 1, 0]]} "Class ", 697, " is:" {{[[1, 2, 3], [0, 0]], [[4, 1, 3, 5, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 1, 3, 5, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 3, 1, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 3, 1, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 1, 3, 5, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 1, 3, 5, 2], [1, 1, 0, 1]]} "Class ", 698, " is:" {{[[1, 2, 3], [0, 0]], [[4, 1, 5, 3, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 1, 5, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 5, 1, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 1, 3, 4], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 1, 5, 3, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 1, 5, 3, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 1, 5, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 5, 1, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 1, 3, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[4, 1, 5, 3, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 4, 2], {}, {}], [[3, 2, 4, 1], {1, 2}, {}], [[3, 1, 4, 2, 5], {1, 2}, {}], [[3, 1, 5, 2, 4], {1, 2, 3}, {}], [[4, 1, 5, 2, 3], {1, 2, 3}, {}], [[4, 1, 5, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 337, 1911, 12409, 90546, 734558, 6552925, 63783237, 672513158, 7636605893, 92907812298, 1205698164935, 16624586163401, 242710345306527, 3740296008433434, 60673703661648421] "" "Class ", 699, " is:" {{[[1, 2, 3], [0, 0]], [[4, 1, 5, 3, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 1, 5, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 5, 1, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 1, 3, 4], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 1, 5, 3, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 1, 5, 3, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 1, 5, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 5, 1, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 1, 3, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[4, 1, 5, 3, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 4, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 333, 1846, 11650, 82176, 642262, 5501601, 51294750, 516872266, 5598830951, 64868050134, 800522385064, 10482781260791, 145179693017481, 2120137022894051, 32560622918454061] "" "Class ", 700, " is:" {{[[1, 2, 3], [0, 0]], [[4, 1, 5, 3, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 1, 5, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 5, 1, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 1, 3, 4], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 1, 5, 3, 2], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 3, 1, 5, 2], [0, 1, 0, 0]]} "Class ", 701, " is:" {{[[1, 2, 3], [0, 0]], [[4, 1, 5, 3, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 1, 5, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 5, 1, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 1, 3, 4], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 1, 5, 3, 2], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 3, 1, 5, 2], [1, 1, 0, 0]]} "Class ", 702, " is:" {{[[1, 2, 3], [0, 0]], [[4, 1, 5, 3, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 1, 5, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 5, 1, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 1, 3, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 1, 5, 3, 2], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[4, 3, 1, 5, 2], [0, 0, 1, 0]]} "Class ", 703, " is:" {{[[1, 2, 3], [0, 0]], [[4, 1, 5, 3, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 1, 5, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 5, 1, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 1, 3, 4], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 1, 5, 3, 2], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[4, 3, 1, 5, 2], [1, 0, 1, 0]]} "Class ", 704, " is:" {{[[1, 2, 3], [0, 0]], [[4, 1, 5, 3, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 1, 5, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 5, 1, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 1, 3, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 1, 5, 3, 2], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 3, 1, 5, 2], [0, 1, 1, 0]]} "Class ", 705, " is:" {{[[1, 2, 3], [0, 0]], [[4, 1, 5, 3, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 1, 5, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 5, 1, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 1, 3, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 1, 5, 3, 2], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 3, 1, 5, 2], [1, 1, 1, 0]]} "Class ", 706, " is:" {{[[1, 2, 3], [0, 0]], [[4, 1, 5, 3, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 1, 5, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 5, 1, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 1, 3, 4], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 1, 5, 3, 2], [1, 0, 0, 0]]} {[[1, 2, 3], [0, 0]], [[4, 3, 1, 5, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 1, 5, 3, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 1, 5, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 5, 1, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 1, 3, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[4, 3, 1, 5, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 334, 1859, 11769, 83262, 652113, 5595466, 52225186, 526571546, 5704578932, 66073890872, 814838311569, 10659043109315, 147416824189308, 2149178828888961, 32941773664073309] "" "Class ", 707, " is:" {{[[1, 2, 3], [0, 0]], [[4, 1, 5, 3, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 1, 5, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 5, 1, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 1, 3, 4], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 1, 5, 3, 2], [1, 0, 0, 1]]} {[[1, 2, 3], [0, 0]], [[4, 3, 1, 5, 2], [1, 0, 0, 1]]} "Class ", 708, " is:" {{[[1, 2, 3], [0, 0]], [[4, 1, 5, 3, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 1, 5, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 5, 1, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 1, 3, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 1, 5, 3, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 3, 1, 5, 2], [0, 1, 0, 1]]} "Class ", 709, " is:" {{[[1, 2, 3], [0, 0]], [[4, 1, 5, 3, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 1, 5, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 5, 1, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 1, 3, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 1, 5, 3, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 3, 1, 5, 2], [1, 1, 0, 1]]} "Class ", 710, " is:" {{[[1, 2, 3], [0, 0]], [[4, 1, 5, 3, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 1, 5, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 5, 1, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 1, 3, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 1, 5, 3, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[4, 3, 1, 5, 2], [0, 0, 1, 1]]} "Class ", 711, " is:" {{[[1, 2, 3], [0, 0]], [[4, 1, 5, 3, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 1, 5, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 5, 1, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 1, 3, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 1, 5, 3, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[4, 3, 1, 5, 2], [1, 0, 1, 1]]} "Class ", 712, " is:" {{[[1, 2, 3], [0, 0]], [[4, 1, 5, 3, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 1, 5, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 5, 1, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 1, 3, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 1, 5, 3, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 3, 1, 5, 2], [0, 1, 1, 1]]} "Class ", 713, " is:" {{[[1, 2, 3], [0, 0]], [[4, 1, 5, 3, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 3, 1, 5, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 5, 1, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 5, 1, 3, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 1, 5, 3, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 3, 1, 5, 2], [1, 1, 1, 1]]} "Class ", 714, " is:" {{[[1, 2, 3], [0, 0]], [[4, 2, 3, 5, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 3, 4, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 3, 2, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 3, 1, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 2, 3, 5, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 1, 3, 4, 2], [0, 1, 0, 0]]} "Class ", 715, " is:" {{[[1, 2, 3], [0, 0]], [[4, 2, 3, 5, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 3, 4, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 3, 2, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 3, 1, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 2, 3, 5, 1], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 1, 3, 4, 2], [1, 1, 0, 0]]} "Class ", 716, " is:" {{[[1, 2, 3], [0, 0]], [[4, 2, 3, 5, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 3, 4, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 3, 2, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 3, 1, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 2, 3, 5, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 1, 3, 4, 2], [0, 0, 1, 0]]} "Class ", 717, " is:" {{[[1, 2, 3], [0, 0]], [[4, 2, 3, 5, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 3, 1, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 2, 3, 5, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 1, 0]]} "Class ", 718, " is:" {{[[1, 2, 3], [0, 0]], [[4, 2, 3, 5, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 3, 4, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 3, 2, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 3, 1, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 2, 3, 5, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 1, 3, 4, 2], [0, 1, 1, 0]]} "Class ", 719, " is:" {{[[1, 2, 3], [0, 0]], [[4, 2, 3, 5, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 3, 4, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 3, 2, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 3, 1, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 2, 3, 5, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 1, 3, 4, 2], [1, 1, 1, 0]]} "Class ", 720, " is:" {{[[1, 2, 3], [0, 0]], [[4, 2, 3, 5, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 3, 4, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 3, 2, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 3, 1, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 2, 3, 5, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 1, 3, 4, 2], [0, 1, 0, 1]]} "Class ", 721, " is:" {{[[1, 2, 3], [0, 0]], [[4, 2, 3, 5, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 3, 4, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 3, 2, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 3, 1, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 2, 3, 5, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 1, 3, 4, 2], [1, 1, 0, 1]]} "Class ", 722, " is:" {{[[1, 2, 3], [0, 0]], [[4, 2, 3, 5, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 3, 4, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 3, 2, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 3, 1, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 2, 3, 5, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 1, 3, 4, 2], [0, 0, 1, 1]]} "Class ", 723, " is:" {{[[1, 2, 3], [0, 0]], [[4, 2, 3, 5, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 3, 1, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 2, 3, 5, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 1, 1]]} "Class ", 724, " is:" {{[[1, 2, 3], [0, 0]], [[4, 2, 3, 5, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 3, 4, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 3, 2, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 3, 1, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 2, 3, 5, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 1, 3, 4, 2], [0, 1, 1, 1]]} "Class ", 725, " is:" {{[[1, 2, 3], [0, 0]], [[4, 2, 3, 5, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 3, 4, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 3, 2, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 3, 1, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 2, 3, 5, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 1, 3, 4, 2], [1, 1, 1, 1]]} "Class ", 726, " is:" {{[[1, 2, 3], [0, 0]], [[4, 2, 5, 3, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 1, 4, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 5, 2, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 3, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 2, 5, 3, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 2, 5, 3, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 1, 4, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 5, 2, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 3, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[4, 2, 5, 3, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 4, 2], {}, {}], [[3, 2, 4, 1], {1, 2}, {}], [[3, 1, 4, 2, 5], {1, 2}, {}], [[3, 1, 5, 2, 4], {1, 2, 3}, {}], [[4, 1, 5, 2, 3], {1, 2, 3}, {}], [[4, 1, 5, 3, 2], {1, 2, 3}, {}], [[4, 2, 5, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 337, 1916, 12477, 91306, 742862, 6645888, 64875378, 685985923, 7812072670, 95315283513, 1240503465747, 17153641173347, 251154945584815, 3881559298623774, 63146353693491285] "" "Class ", 727, " is:" {{[[1, 2, 3], [0, 0]], [[4, 2, 5, 3, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 3, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 2, 5, 3, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 2, 5, 3, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 3, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[4, 2, 5, 3, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 4, 2], {1, 2}, {[1, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 333, 1848, 11688, 82652, 647669, 5562056, 51985198, 525057157, 5700190428, 66183318083, 818415712343, 10737935523058, 148989890162314, 2179652986881075, 33531783977428767] "" "Class ", 728, " is:" {{[[1, 2, 3], [0, 0]], [[4, 2, 5, 3, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 1, 4, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 5, 2, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 3, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 2, 5, 3, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 3, 1, 4, 2], [0, 1, 0, 0]]} "Class ", 729, " is:" {{[[1, 2, 3], [0, 0]], [[4, 2, 5, 3, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 1, 4, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 5, 2, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 3, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 2, 5, 3, 1], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 3, 1, 4, 2], [1, 1, 0, 0]]} "Class ", 730, " is:" {{[[1, 2, 3], [0, 0]], [[4, 2, 5, 3, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 1, 4, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 5, 2, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 3, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 2, 5, 3, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 3, 1, 4, 2], [0, 0, 1, 0]]} "Class ", 731, " is:" {{[[1, 2, 3], [0, 0]], [[4, 2, 5, 3, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 3, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 2, 5, 3, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 1, 0]]} "Class ", 732, " is:" {{[[1, 2, 3], [0, 0]], [[4, 2, 5, 3, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 1, 4, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 5, 2, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 3, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 2, 5, 3, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 3, 1, 4, 2], [0, 1, 1, 0]]} "Class ", 733, " is:" {{[[1, 2, 3], [0, 0]], [[4, 2, 5, 3, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 1, 4, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 5, 2, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 3, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 2, 5, 3, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 3, 1, 4, 2], [1, 1, 1, 0]]} "Class ", 734, " is:" {{[[1, 2, 3], [0, 0]], [[4, 2, 5, 3, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 1, 4, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 5, 2, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 3, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 2, 5, 3, 1], [1, 0, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 3, 1, 4, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 2, 5, 3, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 1, 4, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 5, 2, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 3, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 3, 1, 4, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 335, 1883, 12090, 87018, 695123, 6095283, 58245878, 602147762, 6697947801, 79748074329, 1012068359114, 13636690299177, 194432955141290, 2924557887863840, 46281742755768579] "" "Class ", 735, " is:" {{[[1, 2, 3], [0, 0]], [[4, 2, 5, 3, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 3, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 2, 5, 3, 1], [1, 0, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 2, 5, 3, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 3, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {2}, {}], [[4, 2, 1, 3], {2}, {[0, 1, 0, 0, 0]}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 331, 1806, 11106, 75499, 562728, 4548857, 39623594, 369404465, 3667889751, 38606961496, 429153686918, 5020633139616, 61634029831052, 791841227386389, 10621511420376495] "" "Class ", 736, " is:" {{[[1, 2, 3], [0, 0]], [[4, 2, 5, 3, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 1, 4, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 5, 2, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 3, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 2, 5, 3, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 3, 1, 4, 2], [0, 1, 0, 1]]} "Class ", 737, " is:" {{[[1, 2, 3], [0, 0]], [[4, 2, 5, 3, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 1, 4, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 5, 2, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 3, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 2, 5, 3, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 3, 1, 4, 2], [1, 1, 0, 1]]} "Class ", 738, " is:" {{[[1, 2, 3], [0, 0]], [[4, 2, 5, 3, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 1, 4, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 5, 2, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 3, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 2, 5, 3, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 3, 1, 4, 2], [0, 0, 1, 1]]} "Class ", 739, " is:" {{[[1, 2, 3], [0, 0]], [[4, 2, 5, 3, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 3, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 2, 5, 3, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 1, 1]]} "Class ", 740, " is:" {{[[1, 2, 3], [0, 0]], [[4, 2, 5, 3, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 1, 4, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 5, 2, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 3, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 2, 5, 3, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 3, 1, 4, 2], [0, 1, 1, 1]]} "Class ", 741, " is:" {{[[1, 2, 3], [0, 0]], [[4, 2, 5, 3, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 1, 4, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 5, 2, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 4, 1, 3, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 2, 5, 3, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 3, 1, 4, 2], [1, 1, 1, 1]]} "Class ", 742, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 3, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 3, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 1, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 3, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 3, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 1, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2, 3}, {}], [[4, 2, 1, 5, 3], {1, 2, 3}, {}], [[4, 3, 1, 5, 2], {1, 2, 3}, {}], [[4, 3, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 337, 1916, 12472, 91216, 741811, 6633460, 64724603, 684080981, 7786838464, 94964339521, 1235374344411, 17074969475908, 249889531038707, 3860250403177347, 62771182869791253] "" "Class ", 743, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 1, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 1, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {[1, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 334, 1859, 11769, 83262, 652113, 5595466, 52225186, 526571546, 5704578932, 66073890872, 814838311569, 10659043109315, 147416824189308, 2149178828888961, 32941773664073309] "" "Class ", 744, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 2, 5, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 3, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 3, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 1, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 2, 5, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 1, 4, 3, 2], [0, 1, 0, 0]]} "Class ", 745, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 2, 5, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 3, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 3, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 1, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 2, 5, 1], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 1, 4, 3, 2], [1, 1, 0, 0]]} "Class ", 746, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 2, 5, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 3, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 3, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 1, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 2, 5, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 1, 4, 3, 2], [0, 0, 1, 0]]} "Class ", 747, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 2, 5, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 1, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 2, 5, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 1, 0]]} "Class ", 748, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 2, 5, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 3, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 3, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 1, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 2, 5, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 1, 4, 3, 2], [0, 1, 1, 0]]} "Class ", 749, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 2, 5, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 3, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 3, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 1, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 2, 5, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 1, 4, 3, 2], [1, 1, 1, 0]]} "Class ", 750, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 3, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 3, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 1, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 1, 4, 3, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 3, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 3, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 1, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 1, 4, 3, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 333, 1851, 11734, 83164, 653474, 5628408, 52774318, 534854138, 5827481628, 67916924999, 843145018824, 11107270044342, 154757667349385, 2273733456177052, 35132434808869785] "" "Class ", 751, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 1, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 1, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 330, 1781, 10733, 70871, 508915, 3934378, 32564514, 286784570, 2675887278, 26341411136, 272671351446, 2958818454730, 33569619092399, 397267521503441, 4893511156602442] "" "Class ", 752, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 3, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 3, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 1, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 1, 4, 3, 2], [0, 1, 0, 1]]} "Class ", 753, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 3, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 3, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 1, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 1, 4, 3, 2], [1, 1, 0, 1]]} "Class ", 754, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 2, 5, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 3, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 3, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 1, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 2, 5, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 1, 4, 3, 2], [0, 0, 1, 1]]} "Class ", 755, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 2, 5, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 1, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 2, 5, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 1, 1]]} "Class ", 756, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 2, 5, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 3, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 3, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 1, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 2, 5, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 1, 4, 3, 2], [0, 1, 1, 1]]} "Class ", 757, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 2, 5, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 1, 4, 3, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 5, 2, 3, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 4, 1, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 2, 5, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 1, 4, 3, 2], [1, 1, 1, 1]]} "Class ", 758, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 5, 3, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 5, 4], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 5, 3, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 5, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {}, {}], [[3, 2, 4, 1, 5], {1, 2}, {}], [[3, 2, 5, 1, 4], {1, 2, 3}, {}], [[4, 2, 5, 1, 3], {1, 2, 3}, {}], [[4, 3, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 341, 1957, 12868, 95122, 781491, 7061867, 69617341, 743488034, 8550990216, 105371164273, 1385019688833, 19342786382061, 286026135071903, 4464506822303877, 73352963122145972] "" "Class ", 759, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 1, 3, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 5, 3, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 5, 4], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 1, 3, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 5, 3, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 5, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 337, 1892, 12099, 86479, 684240, 5932630, 55949056, 570107163, 6242142523, 73083550590, 911140842742, 12050794437949, 168529922886185, 2484778481439559, 38520774655320573] "" "Class ", 760, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 5, 4], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 5, 4], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {2, 3}, {}], [[2, 4, 1, 3], {2, 3}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {3}, {}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 337, 1899, 12227, 88239, 706477, 6207797, 59401917, 614651009, 6837990821, 81377989523, 1031521680353, 13873232302991, 197304030317891, 2958299512142347, 46635996315031743] "" "Class ", 761, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 1, 3, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 5, 3, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 5, 4], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 5, 1, 3, 2], [1, 1, 0, 0]]} "Class ", 762, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 5, 3, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 5, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 0, 1, 0]]} "Class ", 763, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 1, 3, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 5, 3, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 5, 4], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[4, 5, 1, 3, 2], [1, 0, 1, 0]]} "Class ", 764, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 5, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 1, 0]]} "Class ", 765, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 1, 3, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 5, 3, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 5, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 5, 1, 3, 2], [1, 1, 1, 0]]} "Class ", 766, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 5, 3, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 5, 4], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 0, 0]]} {[[1, 2, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 5, 3, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 5, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 340, 1948, 12767, 94126, 770698, 6942047, 68194372, 725686054, 8314988378, 102069489214, 1336322238035, 18587247712367, 273719087416872, 4254432775095552, 69602251085277309] "" "Class ", 767, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 1, 3, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 5, 3, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 5, 4], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 0, 1]]} {[[1, 2, 3], [0, 0]], [[4, 5, 1, 3, 2], [1, 0, 0, 1]]} "Class ", 768, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {2, 3}, {}], [[2, 4, 1, 3], {2, 3}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3, 4}, {[0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 336, 1889, 12116, 87071, 693434, 6056593, 57556147, 591003505, 6519564346, 76878440973, 964868357603, 12839781162389, 180557133439170, 2675100406876797, 41645693047078515] "" "Class ", 769, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 1, 3, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 5, 3, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 5, 1, 3, 2], [1, 1, 0, 1]]} "Class ", 770, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 5, 3, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 5, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 0, 1, 1]]} "Class ", 771, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 1, 3, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 5, 3, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 5, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[4, 5, 1, 3, 2], [1, 0, 1, 1]]} "Class ", 772, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 5, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 1, 1]]} "Class ", 773, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 1, 3, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 5, 3, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 5, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 5, 1, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 5, 1, 3, 2], [1, 1, 1, 1]]} "Class ", 774, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 5, 3, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 5, 3, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {}, {}], [[3, 2, 4, 1, 5], {1, 2}, {}], [[3, 2, 5, 1, 4], {1, 2, 3}, {}], [[4, 2, 5, 1, 3], {1, 2, 3}, {}], [[4, 3, 5, 1, 2], {1, 2, 3}, {}], [[4, 3, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 337, 1916, 12475, 91270, 742436, 6640837, 64814200, 685212044, 7801820818, 95172651272, 1238418565773, 17121654321580, 250640357204162, 3872892191329953, 62993731993279084] "" "Class ", 775, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 333, 1851, 11739, 83228, 654137, 5635635, 52853476, 535774713, 5838668212, 68060581883, 845082798349, 11134773728468, 155167143748376, 2280122968019439, 35236714601534048] "" "Class ", 776, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 1, 4], {3}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 1, 3], {3}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {3}, {}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 333, 1842, 11565, 80948, 625970, 5292091, 48574146, 480742536, 5103451838, 57828887484, 696618480040, 8888281917848, 119736306858068, 1698101764506916, 25287924622313100] "" "Class ", 777, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 5, 3, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [1, 1, 0, 0]]} "Class ", 778, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 5, 3, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 4, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 0, 1, 0]]} "Class ", 779, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 4, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 1, 0]]} "Class ", 780, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 4, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 1, 0]]} "Class ", 781, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 5, 3, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 4, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [1, 1, 1, 0]]} "Class ", 782, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 5, 3, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 5, 3, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 336, 1902, 12314, 89457, 722098, 6403404, 61928082, 648337279, 7307253046, 88197837398, 1135160673486, 15517917657175, 224552939203360, 3429009643357666, 55105957964024116] "" "Class ", 783, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {2}, {}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 332, 1834, 11532, 80760, 624901, 5283680, 48481601, 479475925, 5083988563, 57518021449, 691511613126, 8802746471502, 118270643976400, 1672392239074389, 24825177770267061] "" "Class ", 784, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 1, 4], {3}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 1, 3], {3}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {3, 4}, {[0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 332, 1827, 11393, 79005, 604072, 5037421, 45514873, 442496890, 4605670919, 51073571384, 601070434811, 7480160627249, 98132673391433, 1353348749927617, 19571291616272669] "" "Class ", 785, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 5, 3, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]} "Class ", 786, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 5, 3, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 4, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 0, 1, 1]]} "Class ", 787, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 4, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 1, 1]]} "Class ", 788, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 4, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]} "Class ", 789, " is:" {{[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 5, 3, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 3, 1, 4, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 3, 5, 2, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 4, 1, 3, 2], [1, 1, 1, 1]]} "Class ", 790, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 5, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 3, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 5, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 3, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4}, {}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 341, 1963, 12915, 95589, 785887, 7109075, 70143603, 749824227, 8631728867, 106465196481, 1400692127321, 19579788237903, 289798710712593, 4527579527058603, 74458132820583101] "" "Class ", 791, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 3, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 3, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {[1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 340, 1949, 12777, 94210, 771513, 6950177, 68283585, 726718562, 8327801006, 102238022984, 1338672737531, 18621869154134, 274256381796951, 4263197268726493, 69752180176454757] "" "Class ", 792, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 4, 1, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 5, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 3, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 3, 4, 1, 2], [0, 1, 0, 0]]} "Class ", 793, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 4, 1, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 5, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 3, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 3, 4, 1, 2], [1, 1, 0, 0]]} "Class ", 794, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 5, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 5, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {2, 3}, {}], [[2, 4, 1, 3], {2, 3}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {3}, {}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {3, 4}, {}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 338, 1919, 12442, 90536, 730892, 6479726, 62580240, 653871542, 7348428476, 88380395900, 1132597355984, 15405737634132, 221665330786390, 3363586250750968, 53680153704709730] "" "Class ", 795, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {2, 3}, {}], [[2, 4, 1, 3], {2, 3}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {}, {[1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {3, 4}, {[1, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 337, 1903, 12257, 88449, 707199, 6201313, 59164867, 609953303, 6755757947, 79987986459, 1008009722949, 13469119907101, 190189090090409, 2829444305852463, 44230169631086513] "" "Class ", 796, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 4, 1, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 5, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 3, 4, 1, 2], [0, 1, 1, 0]]} "Class ", 797, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 4, 1, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 5, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 3, 4, 1, 2], [1, 1, 1, 0]]} "Class ", 798, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 5, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 3, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 5, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 3, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 337, 1898, 12179, 87562, 697278, 6093277, 57956274, 596118231, 6592383603, 78002511565, 983253812258, 13154468976406, 186156394333056, 2778301563704644, 43612416052762234] "" "Class ", 799, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 3, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 3, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {2, 3}, {}], [[4, 2, 3, 1], {2, 3}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 336, 1879, 11921, 84348, 658178, 5611755, 51872435, 516550074, 5511218307, 62706944082, 757799968991, 9692059402734, 130777304567757, 1856450207875549, 27655024975183172] "" "Class ", 800, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 4, 1, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 5, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 3, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 3, 4, 1, 2], [0, 1, 0, 1]]} "Class ", 801, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 4, 1, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 5, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 3, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 3, 4, 1, 2], [1, 1, 0, 1]]} "Class ", 802, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 5, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 3, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]} "Class ", 803, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 3, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]} "Class ", 804, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 4, 1, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 5, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 3, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 3, 4, 1, 2], [0, 1, 1, 1]]} "Class ", 805, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 4, 1, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 5, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 4, 3, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 2, 3, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 3, 4, 1, 2], [1, 1, 1, 1]]} "Class ", 806, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 5, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 5, 4], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 5, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 5, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 341, 1938, 12654, 92442, 751406, 6701561, 65206799, 686403051, 7778553335, 94364771277, 1220562308170, 16763933711709, 243687362762228, 3737395424717043, 60314066601517362] "" "Class ", 807, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 5, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 5, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {2, 3}, {}], [[2, 4, 1, 3], {2, 3}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {}, {}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 1, 5], {2, 3, 4}, {}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {2, 3, 4}, {}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {3}, {}], [[4, 5, 2, 1, 3], {3}, {}], [[4, 5, 2, 3, 1], {3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 340, 1941, 12694, 93170, 759888, 6809498, 66536108, 703765138, 8011747404, 97659333188, 1269054643860, 17511758778558, 255723661728572, 3939751533851680, 63859986988071676] "" "Class ", 808, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 5, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 5, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [1, 1, 0, 0]]} "Class ", 809, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 5, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 5, 4], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {2, 3}, {}], [[2, 4, 1, 3], {2, 3}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {3}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {3, 4}, {[0, 0, 1, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 336, 1875, 11898, 84119, 656882, 5602133, 51810765, 515915639, 5501628600, 62516373907, 753883204747, 9612055143819, 129164762206584, 1824071666201177, 27002612283432413] "" "Class ", 810, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 5, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [1, 1, 1, 0]]} "Class ", 811, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 5, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 5, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[4, 5, 3, 1, 2], [1, 1, 0, 1]]} "Class ", 812, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 341, 1962, 12905, 95510, 785091, 7101029, 70052644, 748750363, 8618063723, 106281360737, 1398067753458, 19540253254813, 289171260461551, 4517116320821817, 74275204726858399] "" "Class ", 813, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 337, 1914, 12439, 90737, 735293, 6545970, 63543893, 667686677, 7551649227, 91456329660, 1180920795949, 16194070475617, 235043360650293, 3599641275215786, 58010236043764509] "" "Class ", 814, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4, 5], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 1, 4], {3}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 1, 3], {3}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {}, {}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 1, 5], {3, 4}, {}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {3, 4}, {}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {3}, {}], [[5, 4, 2, 1, 3], {3}, {}], [[5, 4, 2, 3, 1], {3}, {}], [[5, 4, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 336, 1897, 12241, 88541, 710526, 6257040, 60006592, 622269012, 6938182872, 82754641243, 1051346692486, 14172142640194, 202021321414012, 3036113512642297, 47976069781163144] "" "Class ", 815, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 5, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [1, 1, 0, 0]]} "Class ", 816, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {2, 3}, {}], [[2, 4, 1, 3], {2, 3}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {}, {}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 1, 5], {2, 3, 4}, {}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {2, 3, 4}, {}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {3}, {}], [[4, 5, 2, 1, 3], {3}, {}], [[4, 5, 2, 3, 1], {3}, {}], [[4, 5, 3, 1, 2], {3}, {}], [[4, 5, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 337, 1907, 12325, 89357, 718641, 6345269, 61020881, 634731255, 7100143337, 84981492157, 1083593688685, 14663108117977, 209859297472881, 3167070154628963, 50261413655790965] "" "Class ", 817, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {2, 3}, {}], [[2, 4, 1, 3], {2, 3}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {3}, {[1, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {3, 4}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3, 4}, {[1, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 333, 1846, 11637, 81789, 635084, 5386903, 49562090, 491066000, 5211743313, 58953120594, 707835781675, 8987697907469, 120300429830100, 1692537037303519, 24966308479890384] "" "Class ", 818, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 1, 0]]} "Class ", 819, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 5, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]} "Class ", 820, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 337, 1898, 12190, 87777, 700505, 6139344, 58592612, 605073636, 6721110468, 79914731859, 1012682383245, 13624670864655, 193963545011250, 2913001354776351, 46026894832709089] "" "Class ", 821, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {2}, {}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 333, 1832, 11364, 78074, 588840, 4828027, 42757825, 406453498, 4127445339, 44575155416, 510107674432, 6164923370593, 78458941347828, 1048711817118728, 14687881278036814] "" "Class ", 822, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 1, 4], {3}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 1, 3], {3}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {3, 4}, {[0, 0, 1, 0, 0, 0]}], [[5, 4, 2, 3, 1], {3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 332, 1813, 11111, 75056, 553953, 4423854, 37981959, 348442243, 3399494211, 35120524360, 382850108373, 4389629469453, 52791079205705, 664271848606671, 8726249365942188] "" "Class ", 823, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 5, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]} "Class ", 824, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]} "Class ", 825, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]} "Class ", 826, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 1, 1]]} "Class ", 827, " is:" {{[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 5, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[4, 5, 3, 2, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]} "Class ", 828, " is:" {{[[1, 2, 3], [0, 0]], [[5, 2, 3, 4, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 3, 4, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 3, 2, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 3, 2, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[5, 2, 3, 4, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 2, 3, 4, 1], [0, 1, 0, 0]]} "Class ", 829, " is:" {{[[1, 2, 3], [0, 0]], [[5, 2, 3, 4, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 3, 4, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 3, 2, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 3, 2, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[5, 2, 3, 4, 1], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 2, 3, 4, 1], [1, 1, 0, 0]]} "Class ", 830, " is:" {{[[1, 2, 3], [0, 0]], [[5, 2, 3, 4, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 3, 2, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[5, 2, 3, 4, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 1, 0]]} "Class ", 831, " is:" {{[[1, 2, 3], [0, 0]], [[5, 2, 3, 4, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 3, 4, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 3, 2, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 3, 2, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[5, 2, 3, 4, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 2, 3, 4, 1], [1, 1, 1, 0]]} "Class ", 832, " is:" {{[[1, 2, 3], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 2, 3, 4, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 3, 2, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 2, 3, 4, 1], [1, 1, 0, 1]]} "Class ", 833, " is:" {{[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 4, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 2, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 3, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 4, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 2, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 3, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[4, 1, 3, 2, 5], {1, 2, 3}, {}], [[5, 1, 3, 2, 4], {1, 2, 3}, {}], [[5, 1, 4, 2, 3], {1, 2}, {}], [[5, 1, 4, 3, 2], {1, 2, 3}, {}], [[5, 2, 4, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 337, 1921, 12539, 91925, 749557, 6718930, 65726787, 696388673, 7946996345, 97158939920, 1267104188599, 17557312393218, 257593607042147, 3989224910631550, 65031115834036540] "" "Class ", 834, " is:" {{[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 3, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 3, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[1, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 333, 1852, 11754, 83410, 656266, 5660216, 53144864, 539345150, 5884326377, 68670331278, 853605716606, 11259364733584, 157071500383401, 2310522819042366, 35743029421987371] "" "Class ", 835, " is:" {{[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 4, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 2, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 3, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 3, 2, 4, 1], [0, 1, 0, 0]]} "Class ", 836, " is:" {{[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 4, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 2, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 3, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 3, 2, 4, 1], [1, 1, 0, 0]]} "Class ", 837, " is:" {{[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 4, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 2, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 3, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 3, 2, 4, 1], [0, 0, 1, 0]]} "Class ", 838, " is:" {{[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 3, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 1, 0]]} "Class ", 839, " is:" {{[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 4, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 2, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 3, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 3, 2, 4, 1], [0, 1, 1, 0]]} "Class ", 840, " is:" {{[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 4, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 2, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 3, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 3, 2, 4, 1], [1, 1, 1, 0]]} "Class ", 841, " is:" {{[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 4, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 2, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 3, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 4, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 2, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 3, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {}], [[4, 2, 3, 1], {2, 3}, {}], [[4, 1, 3, 2, 5], {1, 2, 3}, {}], [[5, 1, 3, 2, 4], {2, 3}, {}], [[5, 1, 4, 2, 3], {2, 3}, {}], [[5, 1, 4, 3, 2], {2, 3, 4}, {}], [[5, 2, 4, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 335, 1883, 12090, 87018, 695123, 6095283, 58245878, 602147762, 6697947801, 79748074329, 1012068359114, 13636690299177, 194432955141290, 2924557887863840, 46281742755768579] "" "Class ", 842, " is:" {{[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 3, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 3, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {2, 3}, {[1, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 331, 1806, 11106, 75499, 562728, 4548857, 39623594, 369404465, 3667889751, 38606961496, 429153686918, 5020633139616, 61634029831052, 791841227386389, 10621511420376495] "" "Class ", 843, " is:" {{[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 4, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 2, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 3, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 3, 2, 4, 1], [0, 1, 0, 1]]} "Class ", 844, " is:" {{[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 4, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 2, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 3, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 3, 2, 4, 1], [1, 1, 0, 1]]} "Class ", 845, " is:" {{[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 4, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 2, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 3, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 3, 2, 4, 1], [0, 0, 1, 1]]} "Class ", 846, " is:" {{[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 3, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 1, 1]]} "Class ", 847, " is:" {{[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 4, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 2, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 3, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 3, 2, 4, 1], [0, 1, 1, 1]]} "Class ", 848, " is:" {{[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 3, 2, 4, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 4, 2, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 4, 2, 3, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[5, 2, 4, 3, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 3, 2, 4, 1], [1, 1, 1, 1]]} "Class ", 849, " is:" {{[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 3, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 3, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 4, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 3, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 3, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 4, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {}, {}], [[4, 2, 3, 1, 5], {1, 2, 3}, {}], [[5, 2, 3, 1, 4], {1, 2, 3}, {}], [[5, 2, 4, 1, 3], {1, 2}, {}], [[5, 3, 4, 1, 2], {1, 2}, {}], [[5, 3, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 337, 1921, 12537, 91889, 749161, 6714369, 65671757, 695700865, 7937918329, 97033153629, 1265268835409, 17529200784065, 257141633833713, 3981615580244993, 64897105998818421] "" "Class ", 850, " is:" {{[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 4, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 4, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 333, 1857, 11851, 84606, 670345, 5827204, 55176916, 565102599, 6224930705, 73384533867, 921869445938, 12293456305758, 173442282167832, 2581094882706868, 40406032216780167] "" "Class ", 851, " is:" {{[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 4, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 4, 5], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 1, 4], {3}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 1, 3], {3}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {3}, {}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {3, 4}, {}], [[5, 4, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 334, 1867, 11899, 84785, 669453, 5791114, 54506040, 554146094, 6053057314, 70679015530, 878545637224, 11580873479208, 161359030452244, 2369320657585112, 36566348189327068] "" "Class ", 852, " is:" {{[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 3, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 3, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 4, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 4, 2, 3, 1], [1, 1, 0, 0]]} "Class ", 853, " is:" {{[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 3, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 3, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 4, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 4, 2, 3, 1], [0, 0, 1, 0]]} "Class ", 854, " is:" {{[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 4, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 1, 0]]} "Class ", 855, " is:" {{[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 4, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 1, 0]]} "Class ", 856, " is:" {{[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 3, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 3, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 4, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 4, 2, 3, 1], [1, 1, 1, 0]]} "Class ", 857, " is:" {{[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 3, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 3, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 3, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 3, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {2, 3}, {}], [[4, 2, 3, 1], {}, {}], [[4, 2, 3, 1, 5], {1, 2, 3}, {}], [[5, 2, 3, 1, 4], {2, 3}, {}], [[5, 2, 4, 1, 3], {2, 3}, {}], [[5, 3, 4, 1, 2], {2, 3}, {}], [[5, 3, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 336, 1902, 12314, 89457, 722098, 6403404, 61928082, 648337279, 7307253046, 88197837398, 1135160673486, 15517917657175, 224552939203360, 3429009643357666, 55105957964024116] "" "Class ", 858, " is:" {{[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {2, 3}, {}], [[4, 2, 3, 1], {2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 332, 1834, 11532, 80760, 624901, 5283680, 48481601, 479475925, 5083988563, 57518021449, 691511613126, 8802746471502, 118270643976400, 1672392239074389, 24825177770267061] "" "Class ", 859, " is:" {{[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 1, 4], {3}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 1, 3], {3}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {[1, 0, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {3, 4}, {[1, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 333, 1846, 11619, 81416, 629517, 5311689, 48579730, 478200519, 5040406945, 56609165104, 674761486105, 8504886511753, 113001654972044, 1578206709169141, 23110826847493708] "" "Class ", 860, " is:" {{[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]} "Class ", 861, " is:" {{[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 3, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 3, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 4, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [0, 0]], [[5, 4, 2, 3, 1], [0, 0, 1, 1]]} "Class ", 862, " is:" {{[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 4, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 1, 1]]} "Class ", 863, " is:" {{[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 4, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 1, 1]]} "Class ", 864, " is:" {{[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 2, 3, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 4, 3, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 3, 2, 4, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 0]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 4, 2, 3, 1], [1, 1, 1, 1]]} "Class ", 865, " is:" {{[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 334, 1874, 12027, 86393, 689380, 6036376, 57604554, 594763437, 6606799584, 78564472506, 995742426875, 13399979311215, 190816160658207, 2866611505995223, 45308713429072500] "" "Class ", 866, " is:" {{[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 1, 4], {3}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 1, 3], {3}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {}, {}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 1, 5], {3, 4}, {}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {3, 4}, {}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {3}, {}], [[5, 4, 2, 1, 3], {3}, {}], [[5, 4, 2, 3, 1], {3}, {}], [[5, 4, 3, 1, 2], {3}, {}], [[5, 4, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 333, 1850, 11709, 82753, 647404, 5543998, 51612618, 518640409, 5595804763, 64500240724, 791007071315, 10282124152852, 141207776126953, 2042799488960586, 31048931233121831] "" "Class ", 867, " is:" {{[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 4, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]} "Class ", 868, " is:" {{[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 1, 4], {3}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 1, 3], {3}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {3}, {[1, 0, 0, 0, 0]}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {3, 4}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {3, 4}, {[1, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 17, 69, 329, 1771, 10715, 71438, 520914, 4112241, 34928203, 317205878, 3065658830, 31393536031, 339412053699, 3861722639588, 46108739658972, 576287312408107, 7522720946946331] "" "Class ", 869, " is:" {{[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 4, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]} "Class ", 870, " is:" {{[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 0]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [0, 0]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]} "Class ", 871, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]} "Class ", 872, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]} "Class ", 873, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3, 4, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 3, 2, 1], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 1, 3, 4, 5], [0, 0, 1, 1]]} "Class ", 874, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 3, 2, 1], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 1]]} "Class ", 875, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 1, 1]]} "Class ", 876, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 3, 2, 1], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 1, 1]]} "Class ", 877, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2, 4, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 3, 4, 2, 1], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[1, 3, 2, 4, 5], [0, 0, 1, 1]]} "Class ", 878, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 1]]} "Class ", 879, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2, 4, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 3, 4, 2, 1], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 3, 2, 4, 5], [0, 1, 1, 1]]} "Class ", 880, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2, 4, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 3, 2, 4, 5], [1, 1, 1, 1]]} "Class ", 881, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2, 4, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 4, 2, 1], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 1, 2, 4, 5], [0, 0, 1, 1]]} "Class ", 882, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 4, 2, 1], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 1]]} "Class ", 883, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2, 4, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 4, 2, 1], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 1, 2, 4, 5], [0, 1, 1, 1]]} "Class ", 884, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2, 4, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 4, 2, 1], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 1, 2, 4, 5], [1, 1, 1, 1]]} "Class ", 885, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 5, 3, 4], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 5, 3, 4], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 2, 5, 3, 4], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 863, 4006, 20022, 106983, 607689, 3652572, 23140564, 154012165, 1073695795, 7820675472, 59382591443, 469075786319, 3847678058712, 32719151829599] "" "Class ", 886, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 5, 3, 4], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 5, 2, 1], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 5, 3, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 2, 5, 3, 4], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 5, 2, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 2, 5, 3, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 860, 3952, 19395, 100868, 552630, 3174588, 19047731, 118991335, 771851963, 5186797032, 36036705757, 258412135104, 1909551731860, 14521163953769] "" "Class ", 887, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 5, 3, 4], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1, 4, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 5, 3, 4], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 3, 1, 4, 5], [0, 1, 0, 1]]} "Class ", 888, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 5, 3, 4], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1, 4, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 5, 2, 1], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 5, 3, 4], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 3, 1, 4, 5], [1, 1, 0, 1]]} "Class ", 889, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 5, 2, 1], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 1]]} "Class ", 890, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 1]]} "Class ", 891, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1, 4, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 3, 1, 4, 5], [0, 1, 1, 1]]} "Class ", 892, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1, 4, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 5, 2, 1], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 3, 1, 4, 5], [1, 1, 1, 1]]} "Class ", 893, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 4, 1, 2, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 5, 2, 1], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 4, 1, 2, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 5, 2, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 2, 1, 4], {1, 2}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 862, 3986, 19774, 104447, 583930, 3438648, 21243427, 137209458, 923818321, 6467249913, 46968549942, 353171410927, 2744637776149, 22009731486772] "" "Class ", 894, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1, 4, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1, 4, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 859, 3932, 19146, 98351, 529801, 2979353, 17428723, 105750974, 663928928, 4304031184, 28758620609, 197753011767, 1397485945307, 10137161100582] "" "Class ", 895, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1, 4, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 4, 1, 2, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 2, 1, 4, 5], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1, 4, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 4, 1, 2, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[3, 2, 1, 4, 5], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {3}, {}], [[3, 2, 1, 4], {1}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 1, 3], {1}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {1}, {}], [[4, 3, 2, 1], {1}, {}], [[3, 2, 4, 1, 5], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 2, 5, 1, 4], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 2, 5, 1, 3], {2, 3}, {}], [[4, 3, 5, 1, 2], {2, 3}, {}], [[4, 3, 5, 2, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 858, 3915, 18958, 96593, 514575, 2852334, 16388770, 97310251, 595600167, 3750094858, 24248067008, 160780882461, 1091904639662, 7587105049672] "" "Class ", 896, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1, 4, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 4, 1, 2, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 2, 1, 4, 5], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1, 4, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 4, 1, 2, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[3, 2, 1, 4, 5], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {2}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {}], [[2, 4, 3, 1], {}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {3}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 1, 3], {1}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {1}, {}], [[4, 3, 2, 1], {1}, {}], [[2, 4, 3, 1, 5], {2, 3, 5}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 3, 1, 4], {2, 3}, {}], [[2, 5, 4, 1, 3], {2, 3}, {}], [[3, 5, 4, 1, 2], {2, 3}, {}], [[3, 5, 4, 2, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 856, 3875, 18479, 92041, 476290, 2551410, 14110432, 80396532, 471130942, 2835736754, 17511834066, 110851509615, 718718323069, 4769690413227] "" "Class ", 897, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1, 4, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 5, 2, 1], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 2, 1, 4, 5], [0, 0, 1, 1]]} "Class ", 898, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]} "Class ", 899, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1, 4, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 2, 1, 4, 5], [0, 1, 1, 1]]} "Class ", 900, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]} "Class ", 901, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]} "Class ", 902, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 1, 5, 3], {1, 2, 4}, {}], [[3, 4, 1, 5, 2], {1, 2, 4}, {}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 203, 876, 4118, 20841, 112469, 642128, 3853761, 24182852, 157965450, 1070114250, 7494479690, 54116097300, 401956013951, 3064960180277, 23949865217448] "" "Class ", 903, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 2, 4, 3, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 2, 4, 3, 5], [0, 1, 1, 1]]} "Class ", 904, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 2, 4, 3, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 4, 2, 3, 1], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 2, 4, 3, 5], [1, 1, 1, 1]]} "Class ", 905, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 3}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1, 3}, {}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 863, 4001, 19924, 105739, 594361, 3520665, 21884471, 142248226, 963920787, 6791732656, 49644219261, 375687800341, 2938154829063, 23708936906103] "" "Class ", 906, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 2, 3, 1], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 2, 3, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [1, 5, 4, 2, 3], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 5, 4, 3, 2], {3}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 860, 3951, 19373, 100567, 549294, 3141496, 18739010, 116206162, 747142512, 4968939466, 34114754638, 241369475023, 1757185518201, 13144868138587] "" "Class ", 907, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {3}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 862, 3982, 19687, 103253, 570458, 3301222, 19917370, 124799457, 809469329, 5419887379, 37372095432, 264834966743, 1925266539509, 14335251178399] "" "Class ", 908, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3, 5], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3, 5], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {2}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {2, 3}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {3}, {}], [[3, 2, 4, 1], {1, 3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 859, 3931, 19119, 97921, 524460, 2921730, 16858380, 100405010, 615519965, 3874925015, 25001381089, 165049371943, 1113222988121, 7661588927073] "" "Class ", 909, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2, 5, 4], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 2, 3, 1], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2, 5, 4], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3, 5], [0, 0, 1, 1]]} "Class ", 910, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2, 5, 4], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 2, 3, 1], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2, 5, 4], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3, 5], [1, 0, 1, 1]]} "Class ", 911, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2, 5, 4], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2, 5, 4], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3, 5], [0, 1, 1, 1]]} "Class ", 912, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2, 5, 4], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 2, 3, 1], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2, 5, 4], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3, 5], [1, 1, 1, 1]]} "Class ", 913, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 2, 3, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 2, 4, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 4, 3, 1], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[1, 4, 2, 3, 5], [0, 0, 1, 1]]} "Class ", 914, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 2, 3, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 2, 4, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 4, 3, 1], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[1, 4, 2, 3, 5], [1, 0, 1, 1]]} "Class ", 915, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 2, 3, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 2, 4, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 4, 3, 1], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 4, 2, 3, 5], [0, 1, 1, 1]]} "Class ", 916, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 2, 3, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 2, 4, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 4, 3, 1], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 4, 2, 3, 5], [1, 1, 1, 1]]} "Class ", 917, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 2, 3, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 4, 3, 1], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 1, 2, 3, 5], [0, 0, 1, 1]]} "Class ", 918, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 2, 3, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 4, 3, 1], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 1, 2, 3, 5], [1, 0, 1, 1]]} "Class ", 919, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 2, 3, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 4, 3, 1], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 1, 2, 3, 5], [0, 1, 1, 1]]} "Class ", 920, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 2, 3, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 4, 3, 1], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 1, 2, 3, 5], [1, 1, 1, 1]]} "Class ", 921, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 5, 2, 4], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 1, 3, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 1, 4, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 5, 3, 1], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 5, 2, 4], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 4, 1, 3, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 3, 5, 2, 4], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 1, 3, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 1, 4, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 5, 3, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 4, 1, 3, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 864, 4023, 20209, 108735, 623051, 3783852, 24257039, 163574824, 1156767412, 8555740556, 66025225500, 530479453906, 4428838400203, 38353716503610] "" "Class ", 922, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 5, 2, 4], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 1, 3, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 1, 4, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 5, 3, 1], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 5, 2, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 3, 5, 2, 4], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 1, 3, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 1, 4, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 5, 3, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 5, 2, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [1, 5, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 862, 3991, 19870, 105633, 596308, 3558624, 22368535, 147629917, 1020259648, 7365594945, 55429367451, 433982249212, 3528941104140, 29755124287453] "" "Class ", 923, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 5, 2, 4], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 1, 3, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 1, 4, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 5, 3, 1], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 5, 2, 4], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 4, 1, 3, 5], [0, 1, 0, 1]]} "Class ", 924, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 5, 2, 4], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 1, 3, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 1, 4, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 5, 3, 1], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 5, 2, 4], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 4, 1, 3, 5], [1, 1, 0, 1]]} "Class ", 925, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 1, 3, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 1, 4, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 5, 3, 1], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 4, 1, 3, 5], [0, 0, 1, 1]]} "Class ", 926, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 1, 3, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 1, 4, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 5, 3, 1], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[2, 4, 1, 3, 5], [1, 0, 1, 1]]} "Class ", 927, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 1, 3, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 1, 4, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 5, 3, 1], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 4, 1, 3, 5], [0, 1, 1, 1]]} "Class ", 928, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 1, 3, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 1, 4, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 5, 3, 1], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 4, 1, 3, 5], [1, 1, 1, 1]]} "Class ", 929, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 5, 4, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 1, 2, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 5, 3, 1], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 5, 4, 2], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 3, 5, 4, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 1, 2, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 5, 3, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 863, 4006, 20031, 107151, 609657, 3671725, 23312646, 155508864, 1086583205, 7931791791, 60348245413, 477569453899, 3923489155316, 33406838788258] "" "Class ", 930, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 5, 4, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 5, 3, 1], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 5, 4, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 3, 5, 4, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 5, 3, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 5, 4, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 860, 3952, 19395, 100868, 552630, 3174588, 19047731, 118991335, 771851963, 5186797032, 36036705757, 258412135104, 1909551731860, 14521163953769] "" "Class ", 931, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 5, 4, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 1, 2, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 5, 3, 1], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 5, 4, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3, 5], [0, 1, 0, 1]]} "Class ", 932, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 5, 4, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 1, 2, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 5, 3, 1], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 5, 4, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3, 5], [1, 1, 0, 1]]} "Class ", 933, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 1, 2, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 5, 3, 1], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3, 5], [0, 0, 1, 1]]} "Class ", 934, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 1, 2, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 5, 3, 1], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3, 5], [1, 0, 1, 1]]} "Class ", 935, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 1, 2, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 5, 3, 1], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3, 5], [0, 1, 1, 1]]} "Class ", 936, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 3, 1, 2, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 5, 3, 1], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3, 5], [1, 1, 1, 1]]} "Class ", 937, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 2, 3, 5], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 4, 2, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 4, 3, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 3, 2, 4, 1], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 2, 3, 5], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 3, 4, 2, 5], [0, 1, 0, 1]]} "Class ", 938, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 2, 3, 5], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 4, 2, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 4, 3, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 3, 2, 4, 1], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 2, 3, 5], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 3, 4, 2, 5], [1, 1, 0, 1]]} "Class ", 939, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 4, 2, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 4, 3, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 3, 2, 4, 1], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 3, 4, 2, 5], [0, 1, 1, 1]]} "Class ", 940, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 4, 2, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 4, 3, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 3, 2, 4, 1], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 3, 4, 2, 5], [1, 1, 1, 1]]} "Class ", 941, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 2, 5, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 4, 2, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 4, 1, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 2, 4, 1], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 2, 5, 3], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 1, 4, 2, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 4, 2, 5, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 4, 2, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 4, 1, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 2, 4, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[3, 1, 4, 2, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 3}, {}], [[3, 1, 4, 2], {1, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 864, 4019, 20146, 108042, 616272, 3720626, 23678566, 158301487, 1108411070, 8106982879, 61794229353, 489851071581, 4030850257268, 34372588163148] "" "Class ", 942, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 2, 5, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 4, 2, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 4, 1, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 2, 4, 1], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 2, 5, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 4, 2, 5, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 4, 2, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 4, 1, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 2, 4, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 4, 2, 5, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [ [1, 5, 4, 2, 3], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 5, 4, 3, 2], {3}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 861, 3969, 19582, 102587, 567144, 3292317, 19987294, 126468901, 831670342, 5670143318, 39993641385, 291296196817, 2187318735625, 16907788659619] "" "Class ", 943, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 2, 5, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 4, 2, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 4, 1, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 2, 4, 1], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 2, 5, 3], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 1, 4, 2, 5], [0, 1, 0, 1]]} "Class ", 944, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 2, 5, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 4, 2, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 4, 1, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 2, 4, 1], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 2, 5, 3], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 1, 4, 2, 5], [1, 1, 0, 1]]} "Class ", 945, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 2, 5, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 4, 2, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 4, 1, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 2, 4, 1], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 2, 5, 3], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 1, 4, 2, 5], [0, 0, 1, 1]]} "Class ", 946, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 2, 5, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 4, 2, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 4, 1, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 2, 4, 1], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 2, 5, 3], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[3, 1, 4, 2, 5], [1, 0, 1, 1]]} "Class ", 947, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 2, 5, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 4, 2, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 4, 1, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 2, 4, 1], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 2, 5, 3], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 1, 4, 2, 5], [0, 1, 1, 1]]} "Class ", 948, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 2, 5, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 4, 2, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 4, 1, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 2, 4, 1], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 2, 5, 3], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 1, 4, 2, 5], [1, 1, 1, 1]]} "Class ", 949, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 3, 2, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 3, 4, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 3, 4, 1], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[1, 4, 3, 2, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 3, 2, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 3, 4, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 3, 4, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[1, 4, 3, 2, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 864, 4016, 20077, 107107, 605899, 3615572, 22660349, 148618996, 1016791014, 7236923286, 53456923000, 408946188484, 3233901333614, 26391082960430] "" "Class ", 950, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 3, 4, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 3, 4, 1], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 3, 4, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 3, 4, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [1, 5, 4, 2, 3], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 863, 4001, 19917, 105594, 592404, 3498355, 21650945, 139914802, 941163116, 6572178283, 47531160988, 355285488652, 2739772751897, 21761249515981] "" "Class ", 951, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 3, 2, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 3, 4, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 3, 4, 1], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 4, 3, 2, 5], [0, 1, 0, 1]]} "Class ", 952, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 3, 2, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 3, 4, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 3, 4, 1], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 4, 3, 2, 5], [1, 1, 0, 1]]} "Class ", 953, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 3, 2, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 3, 4, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 3, 4, 1], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[1, 4, 3, 2, 5], [0, 0, 1, 1]]} "Class ", 954, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 3, 2, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 3, 4, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 3, 4, 1], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[1, 4, 3, 2, 5], [1, 0, 1, 1]]} "Class ", 955, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 3, 2, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 3, 4, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 3, 4, 1], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 4, 3, 2, 5], [0, 1, 1, 1]]} "Class ", 956, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 3, 2, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 3, 4, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 3, 4, 1], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 4, 3, 2, 5], [1, 1, 1, 1]]} "Class ", 957, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 3, 5, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 3, 1, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 3, 4, 1], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 3, 5, 2], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 4, 3, 5, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 3, 1, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 3, 4, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 3}, {[0, 0, 0, 0, 1]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 864, 4022, 20198, 108637, 622134, 3775038, 24172293, 162759119, 1148867264, 8478490487, 65260632823, 522802506653, 4350503278690, 37540282377803] "" "Class ", 958, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 3, 5, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 3, 1, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 3, 4, 1], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 3, 5, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 4, 3, 5, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 3, 1, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 3, 4, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 4, 3, 5, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [ [1, 5, 4, 2, 3], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 5, 4, 3, 2], {3}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 861, 3969, 19582, 102587, 567144, 3292317, 19987294, 126468901, 831670342, 5670143318, 39993641385, 291296196817, 2187318735625, 16907788659619] "" "Class ", 959, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 3, 5, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 3, 1, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 3, 4, 1], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 3, 5, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2, 5], [0, 1, 0, 1]]} "Class ", 960, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 3, 5, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 3, 1, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 3, 4, 1], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 3, 5, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2, 5], [1, 1, 0, 1]]} "Class ", 961, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 3, 1, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 3, 4, 1], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2, 5], [0, 0, 1, 1]]} "Class ", 962, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 3, 1, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 3, 4, 1], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2, 5], [1, 0, 1, 1]]} "Class ", 963, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 3, 1, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 3, 4, 1], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2, 5], [0, 1, 1, 1]]} "Class ", 964, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 3, 1, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 3, 4, 1], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2, 5], [1, 1, 1, 1]]} "Class ", 965, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 5, 4, 1], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 5, 4, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 866, 4054, 20534, 111696, 648514, 3998361, 26062045, 178911730, 1289209207, 9722697206, 76541833658, 627555682886, 5347413185001, 47267132289674] "" "Class ", 966, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 1, 2, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 5, 4, 1], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 1, 2, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 5, 4, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [1, 5, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 863, 4006, 20018, 106902, 606663, 3641807, 23037050, 153057907, 1065061437, 7742909230, 58679154724, 462648217251, 3788123136357, 32158164536753] "" "Class ", 967, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 1, 2, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 5, 4, 1], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 4, 1, 2, 5], [0, 1, 0, 1]]} "Class ", 968, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 1, 2, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 5, 4, 1], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 4, 1, 2, 5], [1, 1, 0, 1]]} "Class ", 969, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 1, 2, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 5, 4, 1], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 4, 1, 2, 5], [0, 0, 1, 1]]} "Class ", 970, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 1, 2, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 5, 4, 1], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[3, 4, 1, 2, 5], [1, 0, 1, 1]]} "Class ", 971, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 1, 2, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 5, 4, 1], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 4, 1, 2, 5], [0, 1, 1, 1]]} "Class ", 972, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 1, 2, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 5, 4, 1], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 4, 1, 2, 5], [1, 1, 1, 1]]} "Class ", 973, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 5, 4, 1], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 5, 4, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 864, 4022, 20198, 108637, 622134, 3775038, 24172293, 162759119, 1148867264, 8478490487, 65260632823, 522802506653, 4350503278690, 37540282377803] "" "Class ", 974, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 5, 4, 1], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 5, 4, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [1, 5, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 861, 3977, 19742, 104619, 588642, 3501297, 21937838, 144348760, 994759139, 7162675572, 53772574986, 420085316851, 3409109098825, 28692562606127] "" "Class ", 975, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 5, 4, 1], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2, 5], [0, 1, 0, 1]]} "Class ", 976, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 5, 4, 1], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2, 5], [1, 1, 0, 1]]} "Class ", 977, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 5, 4, 1], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2, 5], [0, 0, 1, 1]]} "Class ", 978, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 5, 4, 1], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2, 5], [1, 0, 1, 1]]} "Class ", 979, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 5, 4, 1], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2, 5], [0, 1, 1, 1]]} "Class ", 980, " is:" {{[[1, 2, 3], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 5, 4, 1], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2, 5], [1, 1, 1, 1]]} "Class ", 981, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 2, 3, 4], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 4, 1, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 4, 3, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 2, 5, 1], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 2, 3, 4], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 3, 4, 1, 5], [0, 1, 0, 0]]} "Class ", 982, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 2, 3, 4], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 4, 1, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 4, 3, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 2, 5, 1], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 2, 3, 4], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 3, 4, 1, 5], [1, 1, 0, 0]]} "Class ", 983, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 2, 3, 4], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 4, 1, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 4, 3, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 2, 5, 1], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 2, 3, 4], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 3, 4, 1, 5], [0, 1, 1, 0]]} "Class ", 984, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 2, 3, 4], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 4, 1, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 4, 3, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 2, 5, 1], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 2, 3, 4], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 3, 4, 1, 5], [1, 1, 1, 0]]} "Class ", 985, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 4, 1, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 2, 5, 1], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 3, 4, 1, 5], [0, 1, 0, 1]]} "Class ", 986, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 4, 1, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 2, 5, 1], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 3, 4, 1, 5], [1, 1, 0, 1]]} "Class ", 987, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 4, 1, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 2, 5, 1], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 3, 4, 1, 5], [0, 1, 1, 1]]} "Class ", 988, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 4, 1, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 2, 5, 1], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 3, 4, 1, 5], [1, 1, 1, 1]]} "Class ", 989, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 4, 2, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 4, 2, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 815, 3735, 18496, 98289, 557261, 3353735, 21331364, 142860051, 1004147212, 7386420205, 56717340319, 453584346135, 3770307191206, 32514230077217] "" "Class ", 990, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 4, 2, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 4, 2, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 793, 3562, 17262, 89684, 496894, 2922141, 18165176, 118937554, 817644030, 5885082985, 44237620651, 346498959821, 2822275646421, 23860709047645] "" "Class ", 991, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 4, 2, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 2, 5, 1], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1, 5], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 4, 2, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 2, 5, 1], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1, 5], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {3}, {}], [[3, 2, 4, 1], {}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {2, 3}, {}], [[4, 2, 5, 1, 3], {2, 3}, {}], [[4, 3, 5, 1, 2], {2, 3}, {}], [[4, 3, 5, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 789, 3501, 16626, 83901, 447381, 2509233, 14747216, 90526651, 578787784, 3844788191, 26478798927, 188697741867, 1389109237124, 10547284600663] "" "Class ", 992, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 4, 2, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 2, 5, 1], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 4, 2, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 2, 5, 1], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3}, %1], [[1, 5, 4, 2, 3], {1, 2, 3}, %1], [[1, 5, 4, 3, 2], {4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, %1], [[2, 5, 4, 1, 3], {1, 2, 3}, %1], [[2, 5, 4, 3, 1], {4}, {[0, 0, 0, 0, 0, 1]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 4, 2, 1], {4}, {[0, 0, 0, 0, 0, 1]}]} %1 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 763, 3274, 14919, 71822, 363643, 1928941, 10684957, 61635746, 369367125, 2294751113, 14752036211, 97966837988, 671059309031, 4734822061435] "" "Class ", 993, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 4, 2, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 4, 2, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 4, 1], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 774, 3355, 15430, 74833, 380844, 2025738, 11224073, 64599699, 385292336, 2376530794, 15132762345, 99319527470, 670944865852, 4659403296358] "" "Class ", 994, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 4, 2, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 4, 2, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 748, 3128, 13731, 62969, 300552, 1488704, 7634723, 40464741, 221311617, 1247444859, 7238458309, 43196661875, 264878725516, 1667564565616] "" "Class ", 995, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 4, 2, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 2, 5, 1], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1, 5], [0, 1, 1, 0]]} "Class ", 996, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 4, 2, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 1, 1, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 4, 2, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [2, 5, 4, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [3, 5, 4, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 4, 2, 1], {4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 731, 2950, 12235, 51822, 223191, 974427, 4302645, 19181100, 86211885, 390248055, 1777495635, 8140539950, 37463689775, 173164232965] "" "Class ", 997, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [1, 5, 4, 2, 3], {2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 5, 4, 3, 2], {3}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 801, 3606, 17463, 90405, 497805, 2903160, 17866520, 115661158, 785409784, 5580531907, 41394221510, 319884183321, 2570491485213, 21441670568187] "" "Class ", 998, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[1, 4, 3, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [1, 5, 4, 2, 3], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 5, 4, 3, 2], {3}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 779, 3431, 16199, 81557, 436188, 2469808, 14760224, 92848108, 613228596, 4242552264, 30678533107, 231395807183, 1817022923630, 14827716336496] "" "Class ", 999, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 2, 5, 1], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1, 5], [0, 1, 0, 1]]} "Class ", 1000, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 2, 5, 1], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1, 5], [1, 1, 0, 1]]} "Class ", 1001, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 4, 1], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 774, 3355, 15430, 74833, 380844, 2025738, 11224073, 64599699, 385292336, 2376530794, 15132762345, 99319527470, 670944865852, 4659403296358] "" "Class ", 1002, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 748, 3128, 13731, 62969, 300552, 1488704, 7634723, 40464741, 221311617, 1247444859, 7238458309, 43196661875, 264878725516, 1667564565616] "" "Class ", 1003, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 2, 5, 1], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1, 5], [0, 1, 1, 1]]} "Class ", 1004, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 1, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [2, 5, 4, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [3, 5, 4, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 4, 2, 1], {4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 731, 2950, 12235, 51822, 223191, 974427, 4302645, 19181100, 86211885, 390248055, 1777495635, 8140539950, 37463689775, 173164232965] "" "Class ", 1005, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 4, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 3, 5, 1], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 4, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 3, 5, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 5, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 813, 3711, 18277, 96447, 542214, 3231845, 20338063, 134642017, 934768321, 6787101096, 51411285866, 405391763264, 3321070802701, 28215958527354] "" "Class ", 1006, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 4, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 3, 5, 1], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 4, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 3, 5, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 789, 3499, 16608, 83815, 447289, 2512790, 14803445, 91155779, 585044503, 3903910090, 27025083511, 193707381315, 1435096478925, 10972124319993] "" "Class ", 1007, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 4, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 3, 5, 1], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1, 5], [0, 1, 0, 0]]} "Class ", 1008, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 4, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 3, 5, 1], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1, 5], [1, 1, 0, 0]]} "Class ", 1009, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 4, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 3, 5, 1], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 4, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 3, 5, 1], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 5, 4, 3, 2], {3}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 4, 3, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 786, 3458, 16203, 80311, 418797, 2287568, 13040865, 77352253, 476146324, 3034799869, 19988819454, 135818335121, 950548577932, 6842825911529] "" "Class ", 1010, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 4, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 3, 5, 1], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 4, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 3, 5, 1], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 773, 3336, 15207, 72697, 362447, 1876392, 10051083, 55544661, 315899245, 1845139684, 11048651523, 67719859612, 424287619507, 2714074517843] "" "Class ", 1011, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 4, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 3, 5, 1], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1, 5], [0, 1, 1, 0]]} "Class ", 1012, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 4, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 3, 5, 1], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1, 5], [1, 1, 1, 0]]} "Class ", 1013, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 4, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 3, 5, 1], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 4, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 3, 5, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 799, 3582, 17238, 88493, 482074, 2775237, 16823508, 107064936, 713395543, 4965291679, 36022440846, 271887675081, 2131279620476, 17323532892062] "" "Class ", 1014, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 4, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 3, 5, 1], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 4, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 3, 5, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 773, 3336, 15207, 72697, 362447, 1876392, 10051083, 55544661, 315899245, 1845139684, 11048651523, 67719859612, 424287619507, 2714074517843] "" "Class ", 1015, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 4, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 3, 5, 1], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1, 5], [0, 1, 0, 1]]} "Class ", 1016, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 4, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 3, 5, 1], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1, 5], [1, 1, 0, 1]]} "Class ", 1017, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 3, 5, 1], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 3, 5, 1], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 5, 4, 3, 2], {3}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 4, 3, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 786, 3458, 16203, 80311, 418797, 2287568, 13040865, 77352253, 476146324, 3034799869, 19988819454, 135818335121, 950548577932, 6842825911529] "" "Class ", 1018, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 3, 5, 1], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 3, 5, 1], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 773, 3336, 15207, 72697, 362447, 1876392, 10051083, 55544661, 315899245, 1845139684, 11048651523, 67719859612, 424287619507, 2714074517843] "" "Class ", 1019, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 3, 5, 1], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1, 5], [0, 1, 1, 1]]} "Class ", 1020, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 3, 5, 1], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1, 5], [1, 1, 1, 1]]} "Class ", 1021, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 2, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 3, 5, 1], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 2, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 3, 5, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 816, 3752, 18680, 99956, 571269, 3468488, 22270617, 150636482, 1069720818, 7951899908, 61716320924, 498943665458, 4192992051163, 36559944319253] "" "Class ", 1022, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 2, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 3, 5, 1], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 2, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 3, 5, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}] , [[1, 4, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 792, 3549, 17151, 88858, 491010, 2880532, 17867822, 116767522, 801376130, 5759424112, 43236061421, 338257334914, 2752260963545, 23246888523174] "" "Class ", 1023, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 2, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 3, 5, 1], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1, 5], [0, 1, 0, 0]]} "Class ", 1024, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 2, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 3, 5, 1], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 2, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 3, 5, 1], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}] , [[1, 4, 3, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 5, 4, 3, 2], {4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [ [2, 5, 4, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 5, 4, 3, 1], {4}, {[0, 0, 0, 0, 0, 1]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 4, 2, 1], {4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 747, 3113, 13595, 62004, 294687, 1457167, 7486039, 39900880, 220332523, 1258667936, 7427819387, 45220721440, 283651844705, 1831019274539] "" "Class ", 1025, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 2, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 3, 5, 1], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 2, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 3, 5, 1], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 3, 4, 1], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 791, 3533, 16970, 87119, 475756, 2752618, 16812999, 108073046, 729045955, 5148347450, 37971933864, 291898543398, 2334232485424, 19383607067271] "" "Class ", 1026, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 2, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 3, 5, 1], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 2, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 3, 5, 1], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}] , [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 763, 3270, 14844, 70961, 355673, 1862785, 10165879, 57673186, 339443431, 2068967527, 13039101751, 84846212977, 569306441734, 3934345877165] "" "Class ", 1027, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 2, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 3, 5, 1], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1, 5], [0, 1, 1, 0]]} "Class ", 1028, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 2, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 3, 5, 1], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1, 5], [1, 1, 1, 0]]} "Class ", 1029, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 2, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 3, 5, 1], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 2, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 3, 5, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 2, 4], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 5, 4, 3, 2], {3}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 804, 3646, 17840, 93600, 523826, 3112437, 19555548, 129471900, 900449664, 6559989883, 49935792193, 396274899991, 3271591128177, 28046700193790] "" "Class ", 1030, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 2, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 3, 5, 1], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 2, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 3, 5, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}] , [[1, 4, 3, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [1, 5, 4, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {3}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 779, 3431, 16199, 81557, 436188, 2469808, 14760224, 92848108, 613228596, 4242552264, 30678533107, 231395807183, 1817022923630, 14827716336496] "" "Class ", 1031, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 2, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 3, 5, 1], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1, 5], [0, 1, 0, 1]]} "Class ", 1032, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 2, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 3, 5, 1], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1, 5], [1, 1, 0, 1]]} "Class ", 1033, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 3, 5, 1], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 3, 5, 1], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 3, 4, 1], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 791, 3533, 16970, 87119, 475756, 2752618, 16812999, 108073046, 729045955, 5148347450, 37971933864, 291898543398, 2334232485424, 19383607067271] "" "Class ", 1034, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 3, 5, 1], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 3, 5, 1], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}] , [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 763, 3270, 14844, 70961, 355673, 1862785, 10165879, 57673186, 339443431, 2068967527, 13039101751, 84846212977, 569306441734, 3934345877165] "" "Class ", 1035, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 3, 5, 1], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1, 5], [0, 1, 1, 1]]} "Class ", 1036, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 3, 5, 1], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1, 5], [1, 1, 1, 1]]} "Class ", 1037, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 4, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 5, 1], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 4, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 5, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 827, 3840, 19322, 104538, 604233, 3710827, 24102386, 164913630, 1184618978, 8907002209, 69915493129, 571597425343, 4857081779080, 42816696287830] "" "Class ", 1038, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 4, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 5, 1], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 4, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 5, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 789, 3499, 16608, 83815, 447289, 2512790, 14803445, 91155779, 585044503, 3903910090, 27025083511, 193707381315, 1435096478925, 10972124319993] "" "Class ", 1039, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 4, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 5, 1], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1, 5], [0, 1, 0, 0]]} "Class ", 1040, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 4, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 5, 1], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1, 5], [1, 1, 0, 0]]} "Class ", 1041, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 4, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 5, 1], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1, 5], [0, 0, 1, 0]]} "Class ", 1042, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 4, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 5, 1], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 4, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 5, 1], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 187, 717, 2829, 11394, 46636, 193434, 811351, 3435914, 14671104, 63096321, 273074930, 1188439542, 5197835892, 22834551207, 100715096277] "" "Class ", 1043, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 4, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 5, 1], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1, 5], [0, 1, 1, 0]]} "Class ", 1044, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 4, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 5, 1], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1, 5], [1, 1, 1, 0]]} "Class ", 1045, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 5, 1], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 5, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {3}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 814, 3728, 18473, 98358, 559481, 3382999, 21650472, 146090400, 1035858809, 7694930941, 59727617082, 483252109919, 4066930426245, 35531294937988] "" "Class ", 1046, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 5, 1], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 5, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 773, 3336, 15207, 72697, 362447, 1876392, 10051083, 55544661, 315899245, 1845139684, 11048651523, 67719859612, 424287619507, 2714074517843] "" "Class ", 1047, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 5, 1], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1, 5], [0, 1, 0, 1]]} "Class ", 1048, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 5, 1], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1, 5], [1, 1, 0, 1]]} "Class ", 1049, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 5, 1], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1, 5], [0, 0, 1, 1]]} "Class ", 1050, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 5, 1], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 5, 1], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 187, 717, 2829, 11394, 46636, 193434, 811351, 3435914, 14671104, 63096321, 273074930, 1188439542, 5197835892, 22834551207, 100715096277] "" "Class ", 1051, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 5, 1], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1, 5], [0, 1, 1, 1]]} "Class ", 1052, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 5, 1], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1, 5], [1, 1, 1, 1]]} "Class ", 1053, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [1, 5, 4, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 5, 4, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 803, 3632, 17693, 92176, 510539, 2990956, 18454256, 119482501, 809194190, 5716576147, 42023936165, 320771707150, 2537426510046, 20765069924647] "" "Class ", 1054, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 766, 3310, 15209, 73930, 378632, 2035793, 11456691, 67302295, 411702314, 2616730129, 17245786983, 117641249719, 829213044143, 6030393688963] "" "Class ", 1055, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 3, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 5, 1], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1, 5], [0, 1, 0, 0]]} "Class ", 1056, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 3, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 5, 1], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1, 5], [1, 1, 0, 0]]} "Class ", 1057, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 3, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 1, 0]]} "Class ", 1058, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 3, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 3, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 186, 707, 2768, 11096, 45340, 188160, 790836, 3359325, 14399097, 62200512, 270514313, 1183492058, 5205018050, 22999189082, 102053134118] "" "Class ", 1059, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 3, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 5, 1], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1, 5], [0, 1, 1, 0]]} "Class ", 1060, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 3, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 5, 1], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1, 5], [1, 1, 1, 0]]} "Class ", 1061, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [1, 5, 4, 2, 3], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 5, 4, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 800, 3584, 17201, 87826, 474191, 2694367, 16046981, 99825694, 646704191, 4351681369, 30345757394, 218850111586, 1629366306636, 12502811341795] "" "Class ", 1062, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 763, 3261, 14698, 69401, 341514, 1744183, 9214255, 50211788, 281587189, 1621867359, 9577778850, 57903995119, 357908271929, 2259145743696] "" "Class ", 1063, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 5, 1], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1, 5], [0, 1, 0, 1]]} "Class ", 1064, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 5, 1], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1, 5], [1, 1, 0, 1]]} "Class ", 1065, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]} "Class ", 1066, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 186, 707, 2768, 11096, 45340, 188160, 790836, 3359325, 14399097, 62200512, 270514313, 1183492058, 5205018050, 22999189082, 102053134118] "" "Class ", 1067, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 5, 1], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1, 5], [0, 1, 1, 1]]} "Class ", 1068, " is:" {{[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 5, 1], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]} "Class ", 1069, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3, 4, 5], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 2, 3, 5, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3, 4, 5], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 2, 3, 5, 4], [0, 1, 1, 0]]} "Class ", 1070, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3, 4, 5], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 2, 3, 5, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3, 4, 5], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 2, 3, 5, 4], [1, 1, 1, 0]]} "Class ", 1071, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3, 4, 5], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 2, 3, 5, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 3, 2, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3, 4, 5], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 2, 3, 5, 4], [0, 1, 1, 1]]} "Class ", 1072, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3, 4, 5], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 2, 3, 5, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 3, 2, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3, 4, 5], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 2, 3, 5, 4], [1, 1, 1, 1]]} "Class ", 1073, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3, 5, 4], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3, 5, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3, 5, 4], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 1, 3, 5, 4], [0, 0, 1, 0]]} "Class ", 1074, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3, 5, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3, 5, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 1, 5, 4, 3], {4}, {[0, 0, 0, 0, 0, 1]}], [[3, 1, 5, 4, 2], {2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 2, 5, 4, 1], {2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 861, 3971, 19624, 103147, 573285, 3353308, 20562166, 131745124, 879549541, 6103840204, 43939436111, 327502981018, 2523346943480, 20068115109545] "" "Class ", 1075, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3, 5, 4], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3, 5, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3, 5, 4], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 1, 3, 5, 4], [0, 1, 1, 0]]} "Class ", 1076, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3, 5, 4], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3, 5, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 3, 1, 2], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3, 5, 4], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 1, 3, 5, 4], [1, 1, 1, 0]]} "Class ", 1077, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3, 5, 4], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3, 5, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 3, 1, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3, 5, 4], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 1, 3, 5, 4], [0, 0, 1, 1]]} "Class ", 1078, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3, 5, 4], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3, 5, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 3, 1, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3, 5, 4], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[2, 1, 3, 5, 4], [1, 0, 1, 1]]} "Class ", 1079, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3, 5, 4], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3, 5, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 3, 1, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3, 5, 4], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 1, 3, 5, 4], [0, 1, 1, 1]]} "Class ", 1080, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3, 5, 4], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3, 5, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 3, 1, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 3, 1, 2], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3, 5, 4], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 1, 3, 5, 4], [1, 1, 1, 1]]} "Class ", 1081, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2, 5, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[1, 3, 2, 5, 4], [0, 0, 1, 0]]} "Class ", 1082, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 1, 5, 4, 3], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 1, 5, 4, 2], {2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 2, 5, 4, 1], {2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 863, 3999, 19885, 105226, 588686, 3463168, 21328736, 137006966, 915024673, 6336581917, 45392551053, 335678543524, 2557874162413, 20051471445719] "" "Class ", 1083, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2, 5, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 3, 4, 1, 2], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 3, 2, 5, 4], [0, 1, 1, 0]]} "Class ", 1084, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2, 5, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 3, 4, 1, 2], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 3, 2, 5, 4], [1, 1, 1, 0]]} "Class ", 1085, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2, 5, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[1, 3, 2, 5, 4], [0, 0, 1, 1]]} "Class ", 1086, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 1]]} "Class ", 1087, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2, 5, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 3, 4, 1, 2], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 3, 2, 5, 4], [0, 1, 1, 1]]} "Class ", 1088, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2, 5, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 3, 4, 1, 2], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 3, 2, 5, 4], [1, 1, 1, 1]]} "Class ", 1089, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2, 5, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 4, 1, 2], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 1, 2, 5, 4], [0, 0, 1, 0]]} "Class ", 1090, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2, 5, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 4, 1, 2], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2, 5, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 4, 1, 2], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[2, 1, 5, 4, 3], {4}, {[0, 0, 0, 0, 0, 1]}], [[3, 1, 5, 4, 2], {2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 2, 5, 4, 1], {2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 862, 3988, 19808, 104813, 587247, 3466726, 21475891, 139135257, 939978274, 6605532863, 48179539835, 364042248822, 2844716553741, 22954428161679] "" "Class ", 1091, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2, 5, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 4, 1, 2], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 1, 2, 5, 4], [0, 1, 1, 0]]} "Class ", 1092, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2, 5, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 4, 1, 2], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 1, 2, 5, 4], [1, 1, 1, 0]]} "Class ", 1093, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2, 5, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 2, 1, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 4, 1, 2], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 1, 2, 5, 4], [0, 0, 1, 1]]} "Class ", 1094, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2, 5, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 2, 1, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 4, 1, 2], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[3, 1, 2, 5, 4], [1, 0, 1, 1]]} "Class ", 1095, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2, 5, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 2, 1, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 4, 1, 2], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 1, 2, 5, 4], [0, 1, 1, 1]]} "Class ", 1096, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2, 5, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 2, 1, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 4, 1, 2], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 1, 2, 5, 4], [1, 1, 1, 1]]} "Class ", 1097, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 3, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 3, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 1, 5, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 2, 5, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 823, 3787, 18826, 100413, 571176, 3447384, 21983218, 147563084, 1039322585, 7659090598, 58907015316, 471786818903, 3926794138480, 33904155021714] "" "Class ", 1098, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 5, 1, 2], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 5, 1, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 789, 3498, 16593, 83664, 445971, 2502030, 14718189, 90486387, 579774807, 3862014909, 26687220198, 190936039110, 1411937246232, 10774765224822] "" "Class ", 1099, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 3, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 5, 1, 2], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [0, 1, 0, 0]]} "Class ", 1100, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 3, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 5, 1, 2], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [1, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 3, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 5, 1, 2], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 4}, {}], [[3, 4, 1, 5, 2], {1, 2, 4}, {}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 774, 3351, 15361, 74043, 373270, 1959528, 10673756, 60148231, 349756973, 2094116131, 12885558053, 81349014977, 526150688678, 3481840090140] "" "Class ", 1101, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [0, 0, 1, 0]]} "Class ", 1102, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 774, 3351, 15361, 74043, 373270, 1959528, 10673756, 60148231, 349756973, 2094116131, 12885558053, 81349014977, 526150688678, 3481840090140] "" "Class ", 1103, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 5, 1, 2], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [0, 1, 1, 0]]} "Class ", 1104, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 5, 1, 2], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [1, 1, 1, 0]]} "Class ", 1105, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 3, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 3, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 810, 3669, 17886, 93247, 517138, 3037655, 18829493, 122776289, 839712998, 6008759235, 44883018537, 349235932468, 2825334296172, 23723457874488] "" "Class ", 1106, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 3, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 5, 1, 2], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 3, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 5, 1, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 773, 3337, 15226, 72937, 364960, 1900116, 10261513, 57340073, 330851623, 1967865896, 12048036823, 75832308455, 490158666371, 3250462236986] "" "Class ", 1107, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 3, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 5, 1, 2], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 3, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 5, 1, 2], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 786, 3455, 16157, 79828, 414475, 2251807, 12756912, 75144750, 459145471, 2904137018, 18981839396, 128011946008, 889546078999, 6361655315141] "" "Class ", 1108, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 3, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 5, 1, 2], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 3, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 5, 1, 2], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 759, 3203, 14129, 64645, 304984, 1476932, 7315104, 36948515, 189871563, 990732313, 5240487838, 28060898517, 151925192982, 830830093074] "" "Class ", 1109, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [0, 0, 1, 1]]} "Class ", 1110, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 1]]} "Class ", 1111, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 5, 1, 2], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [0, 1, 1, 1]]} "Class ", 1112, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 5, 1, 2], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 3, 1, 5, 4], [1, 1, 1, 1]]} "Class ", 1113, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1, 5, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 2, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 5, 1, 2], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1, 5, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 2, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 5, 1, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [ [2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}] , [[2, 1, 5, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 5, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 2, 5, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 811, 3683, 18007, 94124, 522858, 3071480, 19001106, 123341860, 837492746, 5932008172, 43724286908, 334664536800, 2654769055886, 21788204133346] "" "Class ", 1114, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1, 5, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 5, 1, 2], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1, 5, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 5, 1, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 777, 3395, 15801, 77870, 404381, 2204011, 12566136, 74733449, 462456421, 2971081694, 19778526258, 136189151771, 968429122567, 7101346113042] "" "Class ", 1115, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1, 5, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 2, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 5, 1, 2], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 2, 1, 5, 4], [0, 1, 0, 0]]} "Class ", 1116, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1, 5, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 2, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 5, 1, 2], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 2, 1, 5, 4], [1, 1, 0, 0]]} "Class ", 1117, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1, 5, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 5, 1, 2], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1, 5, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 5, 1, 2], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 1, 5, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 5, 4, 2], {2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 2, 5, 4, 1], {2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 806, 3619, 17388, 88741, 478138, 2706760, 16032975, 99024681, 635838368, 4233546588, 29163257960, 207433313815, 1520770911291, 11473747086500] "" "Class ", 1118, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1, 5, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1, 5, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[2, 1, 5, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 5, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0]}], [[3, 2, 5, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 774, 3351, 15361, 74043, 373270, 1959528, 10673756, 60148231, 349756973, 2094116131, 12885558053, 81349014977, 526150688678, 3481840090140] "" "Class ", 1119, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1, 5, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 5, 1, 2], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 2, 1, 5, 4], [0, 1, 1, 0]]} "Class ", 1120, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1, 5, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 5, 1, 2], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 2, 1, 5, 4], [1, 1, 1, 0]]} "Class ", 1121, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1, 5, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 2, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 2, 1, 5, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1, 5, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 2, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[3, 2, 1, 5, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 2, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 797, 3546, 16852, 84940, 451519, 2520115, 14714093, 89588702, 567312976, 3727660900, 25363639407, 178388890011, 1294815100089, 9685095694144] "" "Class ", 1122, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1, 5, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 2, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 5, 1, 2], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[3, 2, 1, 5, 4], [1, 0, 0, 1]]} "Class ", 1123, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1, 5, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 2, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 5, 1, 2], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 2, 1, 5, 4], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1, 5, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 2, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 5, 1, 2], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[3, 2, 1, 5, 4], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {3}, {}], [[3, 2, 1, 4], {1}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 1, 3], {1}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {1}, {}], [[4, 3, 2, 1], {1}, {}], [[3, 2, 4, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 2, 5, 1, 4], {2, 3}, {[0, 0, 0, 1, 0, 0]}], [[4, 2, 5, 1, 3], {2, 3}, {}], [[4, 3, 5, 1, 2], {2, 3}, {}], [[4, 3, 5, 2, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 749, 3132, 13681, 61954, 289167, 1384859, 6781069, 33851741, 171883172, 885949423, 4628058657, 24468289314, 130771051788, 705802003188] "" "Class ", 1124, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1, 5, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 2, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 5, 1, 2], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 2, 1, 5, 4], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1, 5, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 2, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 5, 1, 2], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[3, 2, 1, 5, 4], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {2}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {}], [[2, 4, 3, 1], {}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {3}, {}], [[3, 2, 1, 4], {1}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 1, 3], {1}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {1}, {}], [[4, 3, 2, 1], {1}, {}], [[2, 4, 3, 1, 5], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 1, 4], {2, 3}, {}], [[2, 5, 4, 1, 3], {2, 3}, {}], [[3, 5, 4, 1, 2], {2, 3}, {}], [[3, 5, 4, 2, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 187, 720, 2870, 11742, 49024, 208030, 894577, 3889800, 17073329, 75545987, 336622432, 1509162302, 6802665424, 30811521266, 140158482340] "" "Class ", 1125, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1, 5, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 5, 1, 2], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 2, 1, 5, 4], [0, 0, 1, 1]]} "Class ", 1126, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1, 5, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[3, 2, 1, 5, 4], [1, 0, 1, 1]]} "Class ", 1127, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1, 5, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 5, 1, 2], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 2, 1, 5, 4], [0, 1, 1, 1]]} "Class ", 1128, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1, 5, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 5, 1, 2], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 2, 1, 5, 4], [1, 1, 1, 1]]} "Class ", 1129, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 1, 4, 5], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 2, 5, 3, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 5, 2, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 1, 4, 5], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 2, 5, 3, 4], [0, 1, 0, 1]]} "Class ", 1130, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 1, 4, 5], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 2, 5, 3, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 5, 2, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 1, 4, 5], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 2, 5, 3, 4], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 3, 1, 4, 5], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 2, 5, 3, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 5, 2, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[1, 2, 5, 3, 4], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 1, 5, 3], {1, 2, 4}, {}], [[3, 4, 1, 5, 2], {1, 2, 4}, {}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 203, 876, 4118, 20841, 112469, 642128, 3853761, 24182852, 157965450, 1070114250, 7494479690, 54116097300, 401956013951, 3064960180277, 23949865217448] "" "Class ", 1131, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 1, 4, 5], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 2, 5, 3, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 5, 2, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 1, 4, 5], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 2, 5, 3, 4], [0, 1, 1, 1]]} "Class ", 1132, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 1, 4, 5], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 2, 5, 3, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 5, 2, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 4, 1, 3, 2], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 1, 4, 5], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 2, 5, 3, 4], [1, 1, 1, 1]]} "Class ", 1133, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 1, 5, 4], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 5, 3, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 5, 1, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 1, 5, 4], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 1, 5, 3, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 3, 1, 5, 4], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 5, 3, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 5, 1, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 1, 5, 3, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 3}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 3}, {}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 863, 4001, 19924, 105739, 594361, 3520665, 21884471, 142248226, 963920787, 6791732656, 49644219261, 375687800341, 2938154829063, 23708936906103] "" "Class ", 1134, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 1, 5, 4], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 5, 3, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 5, 1, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 1, 3, 2], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 1, 5, 4], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[2, 1, 5, 3, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 3, 1, 5, 4], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 5, 3, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 5, 1, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 1, 3, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 1, 5, 3, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {2}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 3}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 3}, {}], [[3, 2, 4, 1], {1, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 860, 3951, 19373, 100567, 549294, 3141496, 18739010, 116206162, 747142512, 4968939466, 34114754638, 241369475023, 1757185518201, 13144868138587] "" "Class ", 1135, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 1, 5, 4], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 5, 1, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 1, 5, 4], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 3, 1, 5, 4], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 5, 1, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {3}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 862, 3982, 19687, 103253, 570458, 3301222, 19917370, 124799457, 809469329, 5419887379, 37372095432, 264834966743, 1925266539509, 14335251178399] "" "Class ", 1136, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 1, 5, 4], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 5, 3, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 5, 1, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 1, 3, 2], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 1, 5, 4], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 1, 5, 3, 4], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 3, 1, 5, 4], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 5, 3, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 5, 1, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 1, 3, 2], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 1, 5, 3, 4], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {2}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {2, 3}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {3}, {}], [[3, 2, 4, 1], {1, 3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 859, 3931, 19119, 97921, 524460, 2921730, 16858380, 100405010, 615519965, 3874925015, 25001381089, 165049371943, 1113222988121, 7661588927073] "" "Class ", 1137, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 1, 5, 4], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 5, 3, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 5, 1, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 1, 3, 2], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 1, 5, 4], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 1, 5, 3, 4], [0, 0, 1, 1]]} "Class ", 1138, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 1, 5, 4], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 5, 3, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 5, 1, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 1, 3, 2], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 1, 5, 4], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[2, 1, 5, 3, 4], [1, 0, 1, 1]]} "Class ", 1139, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 1, 5, 4], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 5, 3, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 5, 1, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 1, 3, 2], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 1, 5, 4], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 1, 5, 3, 4], [0, 1, 1, 1]]} "Class ", 1140, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 1, 5, 4], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 5, 3, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 5, 1, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 1, 3, 2], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 1, 5, 4], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 1, 5, 3, 4], [1, 1, 1, 1]]} "Class ", 1141, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 4, 1, 5], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 2, 3, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 2, 5, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 4, 3, 2], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 4, 1, 5], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[1, 5, 2, 3, 4], [0, 0, 1, 1]]} "Class ", 1142, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 4, 1, 5], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 2, 3, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 2, 5, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 4, 3, 2], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 4, 1, 5], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[1, 5, 2, 3, 4], [1, 0, 1, 1]]} "Class ", 1143, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 4, 1, 5], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 2, 3, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 2, 5, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 4, 3, 2], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 4, 1, 5], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 5, 2, 3, 4], [0, 1, 1, 1]]} "Class ", 1144, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 4, 1, 5], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 2, 3, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 2, 5, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 4, 3, 2], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 4, 1, 5], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 5, 2, 3, 4], [1, 1, 1, 1]]} "Class ", 1145, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 4, 5, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 2, 3, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 2, 1, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 4, 3, 2], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 4, 5, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 1, 2, 3, 4], [0, 0, 1, 1]]} "Class ", 1146, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 4, 5, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 2, 3, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 2, 1, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 4, 3, 2], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 4, 5, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 1, 2, 3, 4], [1, 0, 1, 1]]} "Class ", 1147, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 4, 5, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 2, 3, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 2, 1, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 4, 3, 2], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 4, 5, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 1, 2, 3, 4], [0, 1, 1, 1]]} "Class ", 1148, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 4, 5, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 4, 5, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]} "Class ", 1149, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 5, 1, 4], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 1, 3, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 1, 5, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 5, 3, 2], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 5, 1, 4], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 5, 1, 3, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 3, 5, 1, 4], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 1, 3, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 1, 5, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 5, 3, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 5, 1, 3, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 864, 4021, 20180, 108451, 620624, 3764181, 24100354, 162325122, 1146679178, 8472798765, 65328102166, 524475959198, 4375795612063, 37872570384142] "" "Class ", 1150, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 5, 1, 4], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 1, 3, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 1, 5, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 5, 3, 2], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 5, 1, 4], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[2, 5, 1, 3, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 3, 5, 1, 4], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 1, 3, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 1, 5, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 5, 3, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 5, 1, 3, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 863, 4005, 20006, 106812, 606125, 3639243, 23030471, 153111640, 1066306717, 7759372128, 58865770545, 464634257927, 3808690179593, 32369155633367] "" "Class ", 1151, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 5, 1, 4], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 1, 3, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 1, 5, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 5, 3, 2], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 5, 1, 4], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 5, 1, 3, 4], [0, 1, 0, 1]]} "Class ", 1152, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 5, 1, 4], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 1, 3, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 1, 5, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 5, 3, 2], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 5, 1, 4], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 5, 1, 3, 4], [1, 1, 0, 1]]} "Class ", 1153, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 5, 1, 4], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 1, 3, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 1, 5, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 5, 3, 2], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 5, 1, 4], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 5, 1, 3, 4], [0, 0, 1, 1]]} "Class ", 1154, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 5, 1, 4], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 1, 3, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 1, 5, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 5, 3, 2], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 5, 1, 4], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[2, 5, 1, 3, 4], [1, 0, 1, 1]]} "Class ", 1155, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 5, 1, 4], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 1, 3, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 1, 5, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 5, 3, 2], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 5, 1, 4], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 5, 1, 3, 4], [0, 1, 1, 1]]} "Class ", 1156, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 5, 1, 4], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 1, 3, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 1, 5, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 5, 3, 2], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 5, 1, 4], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 5, 1, 3, 4], [1, 1, 1, 1]]} "Class ", 1157, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 5, 4, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 1, 3, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 1, 2, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 5, 3, 2], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 5, 4, 1], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 2, 1, 3, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 3, 5, 4, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 1, 3, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 1, 2, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 5, 3, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 2, 1, 3, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 863, 4010, 20092, 107776, 615273, 3719979, 23722254, 158993174, 1116524588, 8193104426, 62672690644, 498689588951, 4119756460011, 35273590545032] "" "Class ", 1158, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 5, 4, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 1, 2, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 5, 4, 1], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 3, 5, 4, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 1, 2, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {3}, {}], [[4, 2, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 860, 3952, 19395, 100868, 552630, 3174588, 19047731, 118991335, 771851963, 5186797032, 36036705757, 258412135104, 1909551731860, 14521163953769] "" "Class ", 1159, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 5, 4, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 1, 3, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 1, 2, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 5, 3, 2], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 5, 4, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 2, 1, 3, 4], [0, 1, 0, 1]]} "Class ", 1160, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 5, 4, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 1, 3, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 1, 2, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 5, 3, 2], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 5, 4, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 2, 1, 3, 4], [1, 1, 0, 1]]} "Class ", 1161, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 5, 4, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 1, 3, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 1, 2, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 5, 3, 2], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 5, 4, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 2, 1, 3, 4], [0, 0, 1, 1]]} "Class ", 1162, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 5, 4, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 1, 3, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 1, 2, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 5, 3, 2], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 5, 4, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 2, 1, 3, 4], [1, 0, 1, 1]]} "Class ", 1163, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 5, 4, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 1, 3, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 1, 2, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 5, 3, 2], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 5, 4, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 2, 1, 3, 4], [0, 1, 1, 1]]} "Class ", 1164, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 5, 4, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 1, 3, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 3, 1, 2, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 5, 3, 2], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 5, 4, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 2, 1, 3, 4], [1, 1, 1, 1]]} "Class ", 1165, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 1, 3, 5], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 5, 2, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 5, 3, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 3, 1, 4, 2], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 1, 3, 5], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 3, 5, 2, 4], [0, 1, 0, 1]]} "Class ", 1166, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 1, 3, 5], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 5, 2, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 5, 3, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 3, 1, 4, 2], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 1, 3, 5], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 3, 5, 2, 4], [1, 1, 0, 1]]} "Class ", 1167, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 1, 3, 5], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 5, 2, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 5, 3, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 3, 1, 4, 2], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 1, 3, 5], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 3, 5, 2, 4], [0, 1, 1, 1]]} "Class ", 1168, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 1, 3, 5], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 5, 2, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 5, 3, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 3, 1, 4, 2], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 1, 3, 5], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 3, 5, 2, 4], [1, 1, 1, 1]]} "Class ", 1169, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 1, 5, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 5, 2, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 5, 1, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 1, 4, 2], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 1, 5, 3], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 1, 5, 2, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 4, 1, 5, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 5, 2, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 5, 1, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 1, 4, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[3, 1, 5, 2, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 3}, {}], [[3, 1, 4, 2], {1, 3}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 864, 4019, 20146, 108042, 616272, 3720626, 23678566, 158301487, 1108411070, 8106982879, 61794229353, 489851071581, 4030850257268, 34372588163148] "" "Class ", 1170, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 1, 5, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 5, 2, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 5, 1, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 1, 4, 2], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 1, 5, 3], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[3, 1, 5, 2, 4], [1, 0, 0, 1]]} "Class ", 1171, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 1, 5, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 5, 2, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 5, 1, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 1, 4, 2], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 1, 5, 3], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 1, 5, 2, 4], [0, 1, 0, 1]]} "Class ", 1172, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 1, 5, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 5, 2, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 5, 1, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 1, 4, 2], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 1, 5, 3], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 1, 5, 2, 4], [1, 1, 0, 1]]} "Class ", 1173, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 1, 5, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 5, 2, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 5, 1, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 1, 4, 2], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 1, 5, 3], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 1, 5, 2, 4], [0, 0, 1, 1]]} "Class ", 1174, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 1, 5, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 5, 2, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 5, 1, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 1, 4, 2], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 1, 5, 3], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[3, 1, 5, 2, 4], [1, 0, 1, 1]]} "Class ", 1175, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 1, 5, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 5, 2, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 5, 1, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 1, 4, 2], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 1, 5, 3], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 1, 5, 2, 4], [0, 1, 1, 1]]} "Class ", 1176, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 1, 5, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 5, 2, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 5, 1, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 1, 4, 2], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 1, 5, 3], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 1, 5, 2, 4], [1, 1, 1, 1]]} "Class ", 1177, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 3, 1, 5], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 3, 2, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 3, 5, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 3, 4, 2], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 3, 1, 5], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[1, 5, 3, 2, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 4, 3, 1, 5], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 3, 2, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 3, 5, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 3, 4, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[1, 5, 3, 2, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {4}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 864, 4016, 20077, 107107, 605899, 3615572, 22660349, 148618996, 1016791014, 7236923286, 53456923000, 408946188484, 3233901333614, 26391082960430] "" "Class ", 1178, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 3, 1, 5], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 3, 2, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 3, 5, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 3, 4, 2], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 3, 1, 5], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[1, 5, 3, 2, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 4, 3, 1, 5], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 3, 2, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 3, 5, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 3, 4, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[1, 5, 3, 2, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 863, 4001, 19917, 105594, 592404, 3498355, 21650945, 139914802, 941163116, 6572178283, 47531160988, 355285488652, 2739772751897, 21761249515981] "" "Class ", 1179, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 3, 1, 5], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 3, 2, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 3, 5, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 3, 4, 2], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 3, 1, 5], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 5, 3, 2, 4], [0, 1, 0, 1]]} "Class ", 1180, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 3, 1, 5], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 3, 2, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 3, 5, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 3, 4, 2], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 3, 1, 5], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 5, 3, 2, 4], [1, 1, 0, 1]]} "Class ", 1181, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 3, 1, 5], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 3, 2, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 3, 5, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 3, 4, 2], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 3, 1, 5], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[1, 5, 3, 2, 4], [0, 0, 1, 1]]} "Class ", 1182, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 3, 1, 5], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 3, 2, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 3, 5, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 3, 4, 2], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 3, 1, 5], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[1, 5, 3, 2, 4], [1, 0, 1, 1]]} "Class ", 1183, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 3, 1, 5], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 3, 2, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 3, 5, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 3, 4, 2], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 3, 1, 5], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 5, 3, 2, 4], [0, 1, 1, 1]]} "Class ", 1184, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 3, 1, 5], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 3, 2, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 3, 5, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 3, 4, 2], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 3, 1, 5], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 5, 3, 2, 4], [1, 1, 1, 1]]} "Class ", 1185, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 3, 5, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 3, 2, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 3, 1, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 3, 4, 2], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 3, 5, 1], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 1, 3, 2, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 4, 3, 5, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 3, 2, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 3, 1, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 3, 4, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 1, 3, 2, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 3}, {[0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 864, 4026, 20257, 109237, 627540, 3821562, 24566373, 166098061, 1177446965, 8727119151, 67466899214, 542816230810, 4536340922899, 39307939237185] "" "Class ", 1186, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 3, 5, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 3, 2, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 3, 1, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 3, 4, 2], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 3, 5, 1], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 1, 3, 2, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 4, 3, 5, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 3, 2, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 3, 1, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 3, 4, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 1, 3, 2, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {[0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 861, 3969, 19582, 102587, 567144, 3292317, 19987294, 126468901, 831670342, 5670143318, 39993641385, 291296196817, 2187318735625, 16907788659619] "" "Class ", 1187, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 3, 5, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 3, 2, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 3, 1, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 3, 4, 2], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 3, 5, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 1, 3, 2, 4], [0, 1, 0, 1]]} "Class ", 1188, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 3, 5, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 3, 2, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 3, 1, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 3, 4, 2], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 3, 5, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 1, 3, 2, 4], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 4, 3, 5, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 3, 2, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 3, 1, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 3, 4, 2], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 1, 3, 2, 4], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {}, {}], [[3, 2, 4, 1], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {3}, {[0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {2, 3}, {}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {4}, {}], [[3, 1, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 5, 4, 2], {4}, {}], [[3, 2, 5, 4, 1], {1, 2, 4}, {}], [[4, 1, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 5, 3, 2], {4}, {[0, 0, 0, 1, 0, 0]}], [[4, 2, 5, 3, 1], {1, 2, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 859, 3931, 19119, 97921, 524460, 2921730, 16858380, 100405010, 615519965, 3874925015, 25001381089, 165049371943, 1113222988121, 7661588927073] "" "Class ", 1189, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 3, 5, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 3, 2, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 3, 1, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 3, 4, 2], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 3, 5, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 1, 3, 2, 4], [0, 0, 1, 1]]} "Class ", 1190, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 3, 5, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 3, 2, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 3, 1, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 3, 4, 2], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 3, 5, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 1, 3, 2, 4], [1, 0, 1, 1]]} "Class ", 1191, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 3, 5, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 3, 2, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 3, 1, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 3, 4, 2], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 3, 5, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 1, 3, 2, 4], [0, 1, 1, 1]]} "Class ", 1192, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 3, 5, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 3, 2, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 3, 1, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 3, 4, 2], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 3, 5, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 1, 3, 2, 4], [1, 1, 1, 1]]} "Class ", 1193, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 5, 1, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 1, 5, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 5, 4, 2], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 5, 1, 3], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 4, 5, 1, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 1, 5, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 5, 4, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 866, 4053, 20522, 111596, 647762, 3992849, 26021526, 178608955, 1286892528, 9704472673, 76394119001, 626320875911, 5336764148509, 47172400067267] "" "Class ", 1194, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 5, 1, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 1, 2, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 1, 5, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 5, 4, 2], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 5, 1, 3], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[3, 5, 1, 2, 4], [1, 0, 0, 1]]} "Class ", 1195, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 5, 1, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 1, 2, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 1, 5, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 5, 4, 2], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 5, 1, 3], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 5, 1, 2, 4], [0, 1, 0, 1]]} "Class ", 1196, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 5, 1, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 1, 2, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 1, 5, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 5, 4, 2], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 5, 1, 3], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 5, 1, 2, 4], [1, 1, 0, 1]]} "Class ", 1197, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 5, 1, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 1, 2, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 1, 5, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 5, 4, 2], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 5, 1, 3], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 5, 1, 2, 4], [0, 0, 1, 1]]} "Class ", 1198, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 5, 1, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 1, 2, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 1, 5, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 5, 4, 2], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 5, 1, 3], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[3, 5, 1, 2, 4], [1, 0, 1, 1]]} "Class ", 1199, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 5, 1, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 1, 2, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 1, 5, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 5, 4, 2], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 5, 1, 3], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 5, 1, 2, 4], [0, 1, 1, 1]]} "Class ", 1200, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 5, 1, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 1, 2, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 1, 5, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 5, 4, 2], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 5, 1, 3], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 5, 1, 2, 4], [1, 1, 1, 1]]} "Class ", 1201, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 5, 3, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 1, 3, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 5, 4, 2], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 5, 3, 1], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 4, 5, 3, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 1, 3, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 5, 4, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 864, 4026, 20257, 109237, 627540, 3821562, 24566373, 166098061, 1177446965, 8727119151, 67466899214, 542816230810, 4536340922899, 39307939237185] "" "Class ", 1202, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 5, 3, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 1, 3, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 5, 4, 2], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 5, 3, 1], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 4, 5, 3, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 1, 3, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 5, 4, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {3}, {}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {1}, {[0, 0, 0, 1, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 861, 3977, 19742, 104619, 588642, 3501297, 21937838, 144348760, 994759139, 7162675572, 53772574986, 420085316851, 3409109098825, 28692562606127] "" "Class ", 1203, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 5, 3, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 1, 2, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 1, 3, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 5, 4, 2], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 5, 3, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 3, 1, 2, 4], [0, 1, 0, 1]]} "Class ", 1204, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 5, 3, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 1, 2, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 1, 3, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 5, 4, 2], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 5, 3, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 3, 1, 2, 4], [1, 1, 0, 1]]} "Class ", 1205, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 5, 3, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 1, 2, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 1, 3, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 5, 4, 2], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 5, 3, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 3, 1, 2, 4], [0, 0, 1, 1]]} "Class ", 1206, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 5, 3, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 1, 2, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 1, 3, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 5, 4, 2], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 5, 3, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 3, 1, 2, 4], [1, 0, 1, 1]]} "Class ", 1207, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 5, 3, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 1, 2, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 1, 3, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 5, 4, 2], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 5, 3, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 3, 1, 2, 4], [0, 1, 1, 1]]} "Class ", 1208, " is:" {{[[1, 2, 3], [0, 1]], [[2, 4, 5, 3, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 1, 2, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 2, 1, 3, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 5, 4, 2], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 4, 5, 3, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 3, 1, 2, 4], [1, 1, 1, 1]]} "Class ", 1209, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 1, 3, 4], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 5, 1, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 5, 3, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 1, 5, 2], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 1, 3, 4], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 3, 5, 1, 4], [0, 1, 0, 0]]} "Class ", 1210, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 1, 3, 4], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 5, 1, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 5, 3, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 1, 5, 2], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 1, 3, 4], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 3, 5, 1, 4], [1, 1, 0, 0]]} "Class ", 1211, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 1, 3, 4], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 5, 1, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 5, 3, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 1, 5, 2], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 1, 3, 4], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 3, 5, 1, 4], [0, 1, 1, 0]]} "Class ", 1212, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 1, 3, 4], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 5, 1, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 5, 3, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 1, 5, 2], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 1, 3, 4], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 3, 5, 1, 4], [1, 1, 1, 0]]} "Class ", 1213, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 1, 3, 4], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 5, 1, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 5, 3, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 1, 5, 2], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 1, 3, 4], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 3, 5, 1, 4], [0, 1, 0, 1]]} "Class ", 1214, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 1, 3, 4], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 5, 1, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 5, 3, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 1, 5, 2], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 1, 3, 4], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 3, 5, 1, 4], [1, 1, 0, 1]]} "Class ", 1215, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 1, 3, 4], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 5, 1, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 5, 3, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 1, 5, 2], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 1, 3, 4], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 3, 5, 1, 4], [0, 1, 1, 1]]} "Class ", 1216, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 1, 3, 4], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 5, 1, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 5, 3, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 1, 5, 2], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 1, 3, 4], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 3, 5, 1, 4], [1, 1, 1, 1]]} "Class ", 1217, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 5, 2, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 5, 2], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 5, 2, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 5, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 824, 3802, 18981, 101797, 582829, 3543689, 22779959, 154231890, 1096156406, 8154163020, 63324774491, 512219965259, 4306578373903, 37565893052202] "" "Class ", 1218, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 5, 2, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 5, 2], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 5, 2, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 5, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 807, 3686, 18215, 96716, 548442, 3303947, 21051589, 141328284, 996351759, 7354612403, 56694535126, 455354240735, 3802596702496, 32954767220574] "" "Class ", 1219, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 5, 2, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 5, 2], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 0, 1, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 5, 2, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 5, 2], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 813, 3709, 18260, 96359, 541941, 3232725, 20368024, 135065101, 939705640, 6840572215, 51972684729, 411227162685, 3381805969010, 28853156908847] "" "Class ", 1220, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 5, 2, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 5, 2], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 5, 2, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 5, 2], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 794, 3575, 17370, 90465, 502361, 2960475, 18438046, 120926064, 832555209, 6000411082, 45158489989, 354091882583, 2886914319531, 24428575330008] "" "Class ", 1221, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 5, 2, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 5, 2], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [0, 0, 1, 0]]} "Class ", 1222, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 5, 2, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 5, 2], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [1, 0, 1, 0]]} "Class ", 1223, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 5, 2, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 5, 2], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [0, 1, 1, 0]]} "Class ", 1224, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 5, 2, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 5, 2], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [1, 1, 1, 0]]} "Class ", 1225, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 5, 2, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 5, 2], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 5, 2, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 5, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 3}, {}], [[3, 1, 4, 2], {1, 3}, {}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 800, 3594, 17357, 89570, 491495, 2856090, 17514452, 112995539, 764856961, 5418546592, 40086136183, 309045005479, 2478247065754, 20635056103947] "" "Class ", 1226, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 5, 2, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 5, 2], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 5, 2, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 5, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {2}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 3}, {}], [[3, 1, 4, 2], {1, 3}, {}], [[3, 2, 4, 1], {1, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 779, 3431, 16199, 81557, 436188, 2469808, 14760224, 92848108, 613228596, 4242552264, 30678533107, 231395807183, 1817022923630, 14827716336496] "" "Class ", 1227, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 5, 2, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 5, 2], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [0, 1, 0, 1]]} "Class ", 1228, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 5, 2, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 5, 2], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [1, 1, 0, 1]]} "Class ", 1229, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 5, 2, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 5, 2], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 5, 2, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 5, 2], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}], [[3, 1, 4, 2], {}, {}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {4}, {}], [[3, 1, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 5, 4, 2], {4}, {}], [[3, 2, 5, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 1, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 5, 3, 2], {4}, {}], [[4, 2, 5, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 759, 3203, 14129, 64645, 304984, 1476932, 7315104, 36948515, 189871563, 990732313, 5240487838, 28060898517, 151925192982, 830830093074] "" "Class ", 1230, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 5, 2, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 5, 2], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [1, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 5, 2, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 5, 2], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {2}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}], [[3, 1, 4, 2], {}, {}], [[3, 2, 4, 1], {1, 3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {4}, {}], [[3, 1, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 5, 4, 2], {4}, {}], [[3, 2, 5, 4, 1], {1, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 1, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 5, 3, 2], {4}, {}], [[4, 2, 5, 3, 1], {1, 3, 4}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 731, 2950, 12235, 51822, 223191, 974427, 4302645, 19181100, 86211885, 390248055, 1777495635, 8140539950, 37463689775, 173164232965] "" "Class ", 1231, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 5, 2, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 5, 2], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [0, 1, 1, 1]]} "Class ", 1232, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 5, 2, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 5, 2], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 1, 4, 3], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 2, 5, 1, 4], [1, 1, 1, 1]]} "Class ", 1233, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 1, 4], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 3, 1, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 5, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 3, 5, 2], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 3, 1, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 1, 4], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 3, 1, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 5, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 3, 5, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 5, 3, 1, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [3, 5, 4, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 823, 3793, 18890, 100960, 575525, 3481751, 22255589, 149752898, 1057296631, 7810316986, 60213388152, 483383863097, 4032627421860, 34897041086079] "" "Class ", 1234, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 1, 4], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 3, 1, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 5, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 3, 5, 2], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 3, 1, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 1, 4], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 3, 1, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 5, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 3, 5, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 5, 3, 1, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 813, 3713, 18302, 96666, 543909, 3244609, 20434687, 135385345, 940606954, 6834102434, 51800065530, 408700197628, 3350043845873, 28477036002266] "" "Class ", 1235, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 1, 4], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 3, 1, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 5, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 3, 5, 2], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 3, 1, 4], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 5, 3, 1, 4], [0, 1, 0, 0]]} "Class ", 1236, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 1, 4], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 3, 1, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 5, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 3, 5, 2], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 3, 1, 4], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 5, 3, 1, 4], [1, 1, 0, 0]]} "Class ", 1237, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 1, 4], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 3, 1, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 5, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 3, 5, 2], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 3, 1, 4], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 5, 3, 1, 4], [0, 0, 1, 0]]} "Class ", 1238, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 1, 4], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 3, 1, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 5, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 3, 5, 2], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 3, 1, 4], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[2, 5, 3, 1, 4], [1, 0, 1, 0]]} "Class ", 1239, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 1, 4], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 3, 1, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 5, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 3, 5, 2], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 3, 1, 4], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 5, 3, 1, 4], [0, 1, 1, 0]]} "Class ", 1240, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 1, 4], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 3, 1, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 5, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 3, 5, 2], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 3, 1, 4], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 5, 3, 1, 4], [1, 1, 1, 0]]} "Class ", 1241, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 1, 4], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 3, 1, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 5, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 3, 5, 2], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 3, 1, 4], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 5, 3, 1, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 1, 4], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 3, 1, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 5, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 3, 5, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 5, 3, 1, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 799, 3582, 17238, 88493, 482074, 2775237, 16823508, 107064936, 713395543, 4965291679, 36022440846, 271887675081, 2131279620476, 17323532892062] "" "Class ", 1242, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 1, 4], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 3, 1, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 5, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 3, 5, 2], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 3, 1, 4], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[2, 5, 3, 1, 4], [1, 0, 0, 1]]} "Class ", 1243, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 1, 4], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 3, 1, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 5, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 3, 5, 2], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 3, 1, 4], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 5, 3, 1, 4], [0, 1, 0, 1]]} "Class ", 1244, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 1, 4], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 3, 1, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 5, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 3, 5, 2], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 3, 1, 4], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 5, 3, 1, 4], [1, 1, 0, 1]]} "Class ", 1245, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 1, 4], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 3, 1, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 5, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 3, 5, 2], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 3, 1, 4], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 5, 3, 1, 4], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 1, 4], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 3, 1, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 5, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 3, 5, 2], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 5, 3, 1, 4], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {4}, {}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 786, 3458, 16203, 80311, 418797, 2287568, 13040865, 77352253, 476146324, 3034799869, 19988819454, 135818335121, 950548577932, 6842825911529] "" "Class ", 1246, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 1, 4], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 3, 1, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 5, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 3, 5, 2], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 3, 1, 4], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[2, 5, 3, 1, 4], [1, 0, 1, 1]]} "Class ", 1247, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 1, 4], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 3, 1, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 5, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 3, 5, 2], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 3, 1, 4], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 5, 3, 1, 4], [0, 1, 1, 1]]} "Class ", 1248, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 1, 4], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 3, 1, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 5, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 3, 5, 2], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 3, 1, 4], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 5, 3, 1, 4], [1, 1, 1, 1]]} "Class ", 1249, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 3, 5, 2], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 3, 5, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 829, 3861, 19491, 105763, 612786, 3770842, 24533333, 168100488, 1208949257, 9098971616, 71481315325, 584797441596, 4972023474730, 43849752368106] "" "Class ", 1250, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 3, 5, 2], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 3, 5, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}] , [[1, 4, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 804, 3647, 17859, 93776, 525000, 3118423, 19570607, 129299766, 896478299, 6504521297, 49265639647, 388650452321, 3187055858412, 27117351993694] "" "Class ", 1251, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 3, 5, 2], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [0, 1, 0, 0]]} "Class ", 1252, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 3, 5, 2], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 3, 5, 2], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}] , [[1, 4, 3, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0]}], [ [1, 5, 4, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 5, 4, 3, 2], {4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 5, 4, 3, 1], {4}, {[0, 0, 0, 0, 0, 1]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 4, 2, 1], {4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 763, 3275, 14939, 72069, 366097, 1950641, 10864787, 63075096, 380705332, 2383723311, 15453021472, 103540225157, 715924654133, 5101258663518] "" "Class ", 1253, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 3, 5, 2], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [0, 0, 1, 0]]} "Class ", 1254, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 3, 5, 2], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [1, 0, 1, 0]]} "Class ", 1255, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 3, 5, 2], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [0, 1, 1, 0]]} "Class ", 1256, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 3, 5, 2], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [1, 1, 1, 0]]} "Class ", 1257, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 3, 5, 2], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 3, 5, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 3}, {}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 805, 3661, 17999, 95006, 535268, 3202844, 20266819, 135116123, 945984387, 6935288042, 53105040498, 423741642275, 3516118149474, 30283833640190] "" "Class ", 1258, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 3, 5, 2], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 3, 5, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 3, 2], {3}, {}], [[5, 2, 4, 3, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 779, 3431, 16199, 81557, 436188, 2469808, 14760224, 92848108, 613228596, 4242552264, 30678533107, 231395807183, 1817022923630, 14827716336496] "" "Class ", 1259, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 3, 5, 2], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [0, 1, 0, 1]]} "Class ", 1260, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 3, 5, 2], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [1, 1, 0, 1]]} "Class ", 1261, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 3, 5, 2], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 3, 5, 2], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 3, 2], {4}, {}], [[5, 2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 792, 3547, 17116, 88449, 486971, 2843675, 17543335, 113946582, 776826147, 5543704417, 41311665744, 320767016895, 2589938380709, 21706428030664] "" "Class ", 1262, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 3, 5, 2], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [1, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 3, 5, 2], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 3, 2], {4}, {}], [[5, 2, 4, 3, 1], {1, 2, 4}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 763, 3270, 14844, 70961, 355673, 1862785, 10165879, 57673186, 339443431, 2068967527, 13039101751, 84846212977, 569306441734, 3934345877165] "" "Class ", 1263, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 3, 5, 2], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [0, 1, 1, 1]]} "Class ", 1264, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 3, 5, 2], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 3, 4, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 2, 3, 1, 4], [1, 1, 1, 1]]} "Class ", 1265, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 1, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 5, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 5, 2], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 4, 1, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 1, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 5, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 5, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 5, 4, 1, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 836, 3906, 19769, 107551, 624868, 3856048, 25158043, 172859533, 1246587996, 9407658827, 74103239574, 607833385294, 5181130456984, 45808702844648] "" "Class ", 1266, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 1, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 1, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 5, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 5, 2], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 4, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 1, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 1, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 5, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 5, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 5, 4, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 813, 3713, 18302, 96666, 543909, 3244609, 20434687, 135385345, 940606954, 6834102434, 51800065530, 408700197628, 3350043845873, 28477036002266] "" "Class ", 1267, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 1, 3], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 1, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 5, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 5, 2], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 4, 1, 3], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 5, 2, 1, 4], [0, 1, 0, 0]]} "Class ", 1268, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 1, 3], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 1, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 5, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 5, 2], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 4, 1, 3], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 5, 2, 1, 4], [1, 1, 0, 0]]} "Class ", 1269, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 1, 3], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 1, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 5, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 5, 2], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 4, 1, 3], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 5, 2, 1, 4], [0, 0, 1, 0]]} "Class ", 1270, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 1, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 1, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 5, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 5, 2], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 4, 1, 3], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[3, 5, 2, 1, 4], [1, 0, 1, 0]]} "Class ", 1271, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 1, 3], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 1, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 5, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 5, 2], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 4, 1, 3], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 5, 2, 1, 4], [0, 1, 1, 0]]} "Class ", 1272, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 1, 3], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 1, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 5, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 5, 2], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 4, 1, 3], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 5, 2, 1, 4], [1, 1, 1, 0]]} "Class ", 1273, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 1, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 5, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 5, 2], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 4, 1, 3], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 1, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 5, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 5, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 814, 3728, 18473, 98358, 559481, 3382999, 21650472, 146090400, 1035858809, 7694930941, 59727617082, 483252109919, 4066930426245, 35531294937988] "" "Class ", 1274, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 1, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 1, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 5, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 5, 2], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 4, 1, 3], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[3, 5, 2, 1, 4], [1, 0, 0, 1]]} "Class ", 1275, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 1, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 1, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 5, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 5, 2], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 4, 1, 3], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 5, 2, 1, 4], [0, 1, 0, 1]]} "Class ", 1276, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 1, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 1, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 5, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 5, 2], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 4, 1, 3], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 5, 2, 1, 4], [1, 1, 0, 1]]} "Class ", 1277, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 1, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 1, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 5, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 5, 2], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 4, 1, 3], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 5, 2, 1, 4], [0, 0, 1, 1]]} "Class ", 1278, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 1, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 1, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 5, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 5, 2], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 4, 1, 3], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[3, 5, 2, 1, 4], [1, 0, 1, 1]]} "Class ", 1279, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 1, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 1, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 5, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 5, 2], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 4, 1, 3], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 5, 2, 1, 4], [0, 1, 1, 1]]} "Class ", 1280, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 1, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 1, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 5, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 5, 2], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 4, 1, 3], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 5, 2, 1, 4], [1, 1, 1, 1]]} "Class ", 1281, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 3, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 3, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 4, 3, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 3, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 3, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 5, 4, 3, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [1, 5, 4, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 5, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 818, 3769, 18786, 100483, 572925, 3464530, 22124332, 148643945, 1047281888, 7715737728, 59291880509, 474185465396, 3938845410535, 33921489529608] "" "Class ", 1282, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 3, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 3, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 4, 3, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 3, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 3, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 5, 4, 3, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 779, 3426, 16119, 80637, 426673, 2377273, 13894134, 84902834, 540892755, 3583558864, 24636340140, 175406735555, 1291111370197, 9809402422063] "" "Class ", 1283, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 3, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 1, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 3, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 5, 2], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 4, 3, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 3, 2, 1, 4], [0, 1, 0, 0]]} "Class ", 1284, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 3, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 1, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 3, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 5, 2], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 4, 3, 1], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 3, 2, 1, 4], [1, 1, 0, 0]]} "Class ", 1285, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 3, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 1, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 3, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 5, 2], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 4, 3, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 3, 2, 1, 4], [0, 0, 1, 0]]} "Class ", 1286, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 3, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 1, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 3, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 5, 2], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 4, 3, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 3, 2, 1, 4], [1, 0, 1, 0]]} "Class ", 1287, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 3, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 1, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 3, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 5, 2], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 4, 3, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 3, 2, 1, 4], [0, 1, 1, 0]]} "Class ", 1288, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 3, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 1, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 3, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 5, 2], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 4, 3, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 3, 2, 1, 4], [1, 1, 1, 0]]} "Class ", 1289, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 3, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 3, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 4, 3, 1], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 3, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 3, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 4, 3, 1], {1, 2}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 792, 3535, 16914, 86166, 464497, 2636341, 15689680, 97557827, 631845006, 4251208396, 29645060247, 213813263409, 1592082305098, 12218890953967] "" "Class ", 1290, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 3, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 3, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 4, 3, 1], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 3, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 3, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 4, 3, 1], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[4, 1, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 3, 2], {1}, {[0, 0, 0, 0, 1, 0]}], [[5, 2, 4, 3, 1], {1, 2}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 763, 3261, 14698, 69401, 341514, 1744183, 9214255, 50211788, 281587189, 1621867359, 9577778850, 57903995119, 357908271929, 2259145743696] "" "Class ", 1291, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 3, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 1, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 3, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 5, 2], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 4, 3, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 3, 2, 1, 4], [0, 1, 0, 1]]} "Class ", 1292, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 3, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 1, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 3, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 5, 2], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 4, 3, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 3, 2, 1, 4], [1, 1, 0, 1]]} "Class ", 1293, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 3, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 1, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 3, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 5, 2], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 4, 3, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 3, 2, 1, 4], [0, 0, 1, 1]]} "Class ", 1294, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 3, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 1, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 3, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 5, 2], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 4, 3, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 3, 2, 1, 4], [1, 0, 1, 1]]} "Class ", 1295, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 3, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 1, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 3, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 5, 2], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 4, 3, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 3, 2, 1, 4], [0, 1, 1, 1]]} "Class ", 1296, " is:" {{[[1, 2, 3], [0, 1]], [[2, 5, 4, 3, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 1, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[4, 1, 2, 3, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 5, 2], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 5, 4, 3, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 3, 2, 1, 4], [1, 1, 1, 1]]} "Class ", 1297, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 2, 4, 5], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 2, 4, 5, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 4, 2, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 4, 2, 1, 3], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 2, 4, 5], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 2, 4, 5, 3], [0, 1, 1, 0]]} "Class ", 1298, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 2, 4, 5], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 2, 4, 5, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 4, 2, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 4, 2, 1, 3], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 2, 4, 5], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 2, 4, 5, 3], [1, 1, 1, 0]]} "Class ", 1299, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 2, 4, 5], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 2, 4, 5, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 4, 2, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 4, 2, 1, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 2, 4, 5], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 2, 4, 5, 3], [0, 1, 1, 1]]} "Class ", 1300, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 2, 4, 5], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 2, 4, 5, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 4, 2, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 4, 2, 1, 3], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 2, 4, 5], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 2, 4, 5, 3], [1, 1, 1, 1]]} "Class ", 1301, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 2, 5, 4], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 4, 5, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 4, 1, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 2, 1, 3], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 2, 5, 4], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 1, 4, 5, 3], [0, 0, 1, 0]]} "Class ", 1302, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 2, 5, 4], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 4, 5, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 4, 1, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 2, 1, 3], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 2, 5, 4], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[2, 1, 4, 5, 3], [1, 0, 1, 0]]} "Class ", 1303, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 2, 5, 4], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 4, 5, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 4, 1, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 2, 5, 4], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 1, 4, 5, 3], [0, 1, 1, 0]]} "Class ", 1304, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 2, 5, 4], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 4, 5, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 4, 1, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 2, 1, 3], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 2, 5, 4], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 1, 4, 5, 3], [1, 1, 1, 0]]} "Class ", 1305, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 2, 5, 4], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 4, 5, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 4, 1, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 2, 1, 3], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 2, 5, 4], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 1, 4, 5, 3], [0, 0, 1, 1]]} "Class ", 1306, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 2, 5, 4], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 4, 5, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 4, 1, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 2, 1, 3], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 2, 5, 4], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[2, 1, 4, 5, 3], [1, 0, 1, 1]]} "Class ", 1307, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 2, 5, 4], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 4, 5, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 4, 1, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 2, 5, 4], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 1, 4, 5, 3], [0, 1, 1, 1]]} "Class ", 1308, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 2, 5, 4], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 4, 5, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 4, 1, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 2, 1, 3], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 2, 5, 4], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 1, 4, 5, 3], [1, 1, 1, 1]]} "Class ", 1309, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 4, 2, 5], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 2, 5, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 2, 4, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 4, 1, 3], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 4, 2, 5], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[1, 4, 2, 5, 3], [0, 0, 1, 0]]} "Class ", 1310, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 4, 2, 5], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 2, 5, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 2, 4, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 4, 1, 3], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 4, 2, 5], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[1, 4, 2, 5, 3], [1, 0, 1, 0]]} "Class ", 1311, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 4, 2, 5], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 2, 5, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 2, 4, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 4, 1, 3], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 4, 2, 5], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 4, 2, 5, 3], [0, 1, 1, 0]]} "Class ", 1312, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 4, 2, 5], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 2, 5, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 2, 4, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 4, 1, 3], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 4, 2, 5], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 4, 2, 5, 3], [1, 1, 1, 0]]} "Class ", 1313, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 4, 2, 5], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 2, 5, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 2, 4, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 4, 1, 3], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 4, 2, 5], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[1, 4, 2, 5, 3], [0, 0, 1, 1]]} "Class ", 1314, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 4, 2, 5], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 2, 5, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 2, 4, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 4, 1, 3], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 4, 2, 5], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[1, 4, 2, 5, 3], [1, 0, 1, 1]]} "Class ", 1315, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 4, 2, 5], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 2, 5, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 2, 4, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 4, 1, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 4, 2, 5], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 4, 2, 5, 3], [0, 1, 1, 1]]} "Class ", 1316, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 4, 2, 5], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 2, 5, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 2, 4, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 4, 1, 3], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 4, 2, 5], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 4, 2, 5, 3], [1, 1, 1, 1]]} "Class ", 1317, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 4, 5, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 2, 5, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 2, 1, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 4, 1, 3], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 4, 5, 2], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 1, 2, 5, 3], [0, 0, 1, 0]]} "Class ", 1318, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 4, 5, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 2, 5, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 2, 1, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 4, 1, 3], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 4, 5, 2], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 1, 2, 5, 3], [1, 0, 1, 0]]} "Class ", 1319, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 4, 5, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 2, 5, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 2, 1, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 4, 1, 3], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 4, 5, 2], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 1, 2, 5, 3], [0, 1, 1, 0]]} "Class ", 1320, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 4, 5, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 2, 5, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 2, 1, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 4, 1, 3], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 4, 5, 2], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 1, 2, 5, 3], [1, 1, 1, 0]]} "Class ", 1321, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 4, 5, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 2, 5, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 2, 1, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 4, 1, 3], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 4, 5, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 1, 2, 5, 3], [0, 0, 1, 1]]} "Class ", 1322, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 4, 5, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 2, 5, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 2, 1, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 4, 1, 3], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 4, 5, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 1, 2, 5, 3], [1, 0, 1, 1]]} "Class ", 1323, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 4, 5, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 2, 5, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 2, 1, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 4, 1, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 4, 5, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 1, 2, 5, 3], [0, 1, 1, 1]]} "Class ", 1324, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 4, 5, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 2, 5, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 2, 1, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 4, 1, 3], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 4, 5, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 1, 2, 5, 3], [1, 1, 1, 1]]} "Class ", 1325, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 2, 4], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 1, 5, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 4, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 5, 2, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 2, 4], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 1, 5, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 4, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 1, 5, 2, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 1, 5, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[4, 2, 5, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 832, 3856, 19332, 104100, 598191, 3649207, 23530003, 159758418, 1138377801, 8488557135, 66068553443, 535523151446, 4511235715048, 39422594627858] "" "Class ", 1326, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 2, 4], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 1, 5, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 4, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 5, 1, 3], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 5, 2, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 2, 4], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 1, 5, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 4, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 5, 1, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 1, 5, 2, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 813, 3713, 18305, 96709, 544334, 3248289, 20465345, 135639640, 942733683, 6852146896, 51956087677, 410079330514, 3362528603008, 28592880122241] "" "Class ", 1327, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 2, 4], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 1, 5, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 4, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 5, 1, 3], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 5, 2, 4], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 4, 1, 5, 3], [0, 1, 0, 0]]} "Class ", 1328, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 2, 4], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 1, 5, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 4, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 5, 1, 3], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 5, 2, 4], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 4, 1, 5, 3], [1, 1, 0, 0]]} "Class ", 1329, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 2, 4], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 1, 5, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 4, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 5, 1, 3], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 5, 2, 4], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 4, 1, 5, 3], [0, 0, 1, 0]]} "Class ", 1330, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 2, 4], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 1, 5, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 4, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 5, 1, 3], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 5, 2, 4], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[2, 4, 1, 5, 3], [1, 0, 1, 0]]} "Class ", 1331, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 2, 4], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 1, 5, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 4, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 5, 1, 3], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 5, 2, 4], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 4, 1, 5, 3], [0, 1, 1, 0]]} "Class ", 1332, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 2, 4], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 1, 5, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 4, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 5, 1, 3], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 5, 2, 4], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 4, 1, 5, 3], [1, 1, 1, 0]]} "Class ", 1333, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 2, 4], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 1, 5, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 4, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 5, 2, 4], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 4, 1, 5, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 2, 4], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 1, 5, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 4, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 4, 1, 5, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 811, 3680, 17980, 93989, 522781, 3080034, 19149034, 125217659, 858714351, 6159943877, 46115567555, 359546504274, 2913905201211, 24505093569239] "" "Class ", 1334, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 2, 4], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 1, 5, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 4, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 5, 1, 3], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 5, 2, 4], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[2, 4, 1, 5, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 2, 4], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 1, 5, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 4, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 5, 1, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 4, 1, 5, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 787, 3472, 16342, 81507, 428448, 2363239, 13628362, 81916773, 511861177, 3317336484, 22254329002, 154261222225, 1103135662707, 8126680213045] "" "Class ", 1335, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 2, 4], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 1, 5, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 4, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 5, 1, 3], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 5, 2, 4], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 4, 1, 5, 3], [0, 1, 0, 1]]} "Class ", 1336, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 2, 4], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 1, 5, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 4, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 5, 1, 3], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 5, 2, 4], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 4, 1, 5, 3], [1, 1, 0, 1]]} "Class ", 1337, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 2, 4], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 1, 5, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 4, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 5, 1, 3], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 5, 2, 4], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 4, 1, 5, 3], [0, 0, 1, 1]]} "Class ", 1338, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 2, 4], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 1, 5, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 4, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 5, 1, 3], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 5, 2, 4], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[2, 4, 1, 5, 3], [1, 0, 1, 1]]} "Class ", 1339, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 2, 4], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 1, 5, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 4, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 5, 1, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 5, 2, 4], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 4, 1, 5, 3], [0, 1, 1, 1]]} "Class ", 1340, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 2, 4], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 1, 5, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 4, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 5, 1, 3], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 5, 2, 4], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 4, 1, 5, 3], [1, 1, 1, 1]]} "Class ", 1341, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 4, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 1, 5, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 2, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 5, 1, 3], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 5, 4, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 4, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 1, 5, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 2, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 5, 1, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 1, 5, 4, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [ [2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}] , [[2, 1, 5, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 1, 5, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 824, 3802, 18976, 101619, 580186, 3513465, 22468963, 151179402, 1066732835, 7871083827, 60581043842, 485278021208, 4037627925621, 34830519487973] "" "Class ", 1342, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 4, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 1, 5, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 2, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 5, 1, 3], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 5, 4, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 4, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 1, 5, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 2, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 5, 1, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 1, 5, 4, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 789, 3498, 16593, 83664, 445971, 2502030, 14718189, 90486387, 579774807, 3862014909, 26687220198, 190936039110, 1411937246232, 10774765224822] "" "Class ", 1343, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 4, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 1, 5, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 2, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 5, 1, 3], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 5, 4, 2], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 2, 1, 5, 3], [0, 1, 0, 0]]} "Class ", 1344, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 4, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 1, 5, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 2, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 5, 1, 3], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 5, 4, 2], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 2, 1, 5, 3], [1, 1, 0, 0]]} "Class ", 1345, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 4, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 1, 5, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 2, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 5, 1, 3], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 5, 4, 2], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 2, 1, 5, 3], [0, 0, 1, 0]]} "Class ", 1346, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 4, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 1, 5, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 2, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 5, 1, 3], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 5, 4, 2], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 2, 1, 5, 3], [1, 0, 1, 0]]} "Class ", 1347, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 4, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 1, 5, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 2, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 5, 1, 3], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 5, 4, 2], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 2, 1, 5, 3], [0, 1, 1, 0]]} "Class ", 1348, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 4, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 1, 5, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 2, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 5, 1, 3], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 5, 4, 2], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 2, 1, 5, 3], [1, 1, 1, 0]]} "Class ", 1349, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 4, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 1, 5, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 2, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 5, 1, 3], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 5, 4, 2], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 2, 1, 5, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 4, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 1, 5, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 2, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 5, 1, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[4, 2, 1, 5, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 2, 1, 4], {1, 2}, {[0, 0, 1, 0, 0]}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 800, 3590, 17290, 88731, 482404, 2765093, 16642039, 104809426, 688647121, 4708331629, 33420907764, 245792788619, 1869529310843, 14682487562481] "" "Class ", 1350, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 4, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 1, 5, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 2, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 5, 1, 3], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 5, 4, 2], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 2, 1, 5, 3], [1, 0, 0, 1]]} "Class ", 1351, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 4, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 1, 5, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 2, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 5, 1, 3], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 5, 4, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 2, 1, 5, 3], [0, 1, 0, 1]]} "Class ", 1352, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 4, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 1, 5, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 2, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 5, 1, 3], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 5, 4, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 2, 1, 5, 3], [1, 1, 0, 1]]} "Class ", 1353, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 4, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 1, 5, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 2, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 5, 1, 3], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 5, 4, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 2, 1, 5, 3], [0, 0, 1, 1]]} "Class ", 1354, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 4, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 1, 5, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 2, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 5, 1, 3], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 5, 4, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 2, 1, 5, 3], [1, 0, 1, 1]]} "Class ", 1355, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 4, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 1, 5, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 2, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 5, 1, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 5, 4, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 2, 1, 5, 3], [0, 1, 1, 1]]} "Class ", 1356, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 5, 4, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 1, 5, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 5, 1, 2, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 5, 1, 3], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 5, 4, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 2, 1, 5, 3], [1, 1, 1, 1]]} "Class ", 1357, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 1, 4, 5], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 5, 2, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 1, 4, 5], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 0]]} "Class ", 1358, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 1, 4, 5], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 5, 2, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 1, 4, 5], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 0]]} "Class ", 1359, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 1, 4, 5], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 2, 5, 4, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 5, 2, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 1, 4, 5], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 2, 5, 4, 3], [0, 1, 1, 0]]} "Class ", 1360, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 1, 4, 5], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 2, 5, 4, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 5, 2, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 1, 4, 5], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 2, 5, 4, 3], [1, 1, 1, 0]]} "Class ", 1361, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 5, 2, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]} "Class ", 1362, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 5, 2, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 5, 2, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 4}, {[0, 0, 0, 1, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 4}, {}], [[3, 4, 1, 5, 2], {1, 2, 4}, {}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 862, 3982, 19687, 103253, 570458, 3301222, 19917370, 124799457, 809469329, 5419887379, 37372095432, 264834966743, 1925266539509, 14335251178399] "" "Class ", 1363, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 2, 5, 4, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 5, 2, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 2, 5, 4, 3], [0, 1, 1, 1]]} "Class ", 1364, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 2, 5, 4, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 5, 2, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 2, 5, 4, 3], [1, 1, 1, 1]]} "Class ", 1365, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[4, 3, 1, 5, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[4, 3, 2, 5, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 819, 3736, 18345, 96279, 536677, 3161986, 19610050, 127556484, 867524641, 6152428590, 45389744239, 347607854655, 2758138070571, 22635642452092] "" "Class ", 1366, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 1, 2, 3], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 1, 2, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 789, 3495, 16545, 83142, 441009, 2457963, 14339835, 87281820, 552702609, 3632275683, 24719681601, 173880087210, 1261984254525, 9435921363783] "" "Class ", 1367, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {3}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 5, 4, 2], {3, 4}, {}], [[3, 2, 5, 4, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 816, 3700, 18012, 93408, 512836, 2966749, 18007189, 114265524, 755750137, 5196081636, 37050001612, 273413382402, 2084344391670, 16387663763179] "" "Class ", 1368, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 1, 2, 3], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 1, 2, 3], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 789, 3495, 16545, 83142, 441009, 2457963, 14339835, 87281820, 552702609, 3632275683, 24719681601, 173880087210, 1261984254525, 9435921363783] "" "Class ", 1369, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 5, 1, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 1, 2, 3], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [0, 0, 1, 0]]} "Class ", 1370, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 5, 1, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 1, 2, 3], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [1, 0, 1, 0]]} "Class ", 1371, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 5, 1, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [0, 1, 1, 0]]} "Class ", 1372, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 5, 1, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 1, 2, 3], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [1, 1, 1, 0]]} "Class ", 1373, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 5, 1, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 5, 1, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 3}, {[0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {1, 3}, {}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 806, 3613, 17327, 88195, 473677, 2672158, 15770694, 97056098, 621130097, 4123663017, 28341157093, 201275716587, 1474676824635, 11130178351003] "" "Class ", 1374, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 5, 1, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 1, 2, 3], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 5, 1, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 1, 2, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {2}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 3}, {[0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {1, 3}, {}], [[3, 2, 4, 1], {1, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 773, 3336, 15207, 72697, 362447, 1876392, 10051083, 55544661, 315899245, 1845139684, 11048651523, 67719859612, 424287619507, 2714074517843] "" "Class ", 1375, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {3}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 803, 3580, 17011, 85445, 450945, 2487846, 14287340, 85113784, 524416970, 3333334955, 21809961664, 146613104807, 1010887251462, 7138365114780] "" "Class ", 1376, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 5, 1, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 1, 2, 3], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 5, 1, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 1, 2, 3], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {2}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {2, 3}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {3}, {}], [[3, 2, 4, 1], {1, 3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 773, 3336, 15207, 72697, 362447, 1876392, 10051083, 55544661, 315899245, 1845139684, 11048651523, 67719859612, 424287619507, 2714074517843] "" "Class ", 1377, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 5, 1, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 1, 2, 3], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [0, 0, 1, 1]]} "Class ", 1378, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 5, 1, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 1, 2, 3], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [1, 0, 1, 1]]} "Class ", 1379, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 5, 1, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [0, 1, 1, 1]]} "Class ", 1380, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 5, 1, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 5, 1, 2, 3], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 1, 5, 4], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 1, 5, 4, 3], [1, 1, 1, 1]]} "Class ", 1381, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 4, 1, 5], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 2, 4, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 2, 5, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 4, 2, 3], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 4, 1, 5], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[1, 5, 2, 4, 3], [0, 0, 1, 0]]} "Class ", 1382, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 4, 1, 5], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 2, 4, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 2, 5, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 4, 2, 3], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 4, 1, 5], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[1, 5, 2, 4, 3], [1, 0, 1, 0]]} "Class ", 1383, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 4, 1, 5], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 2, 4, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 2, 5, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 4, 2, 3], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 4, 1, 5], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 5, 2, 4, 3], [0, 1, 1, 0]]} "Class ", 1384, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 4, 1, 5], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 2, 4, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 2, 5, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 4, 2, 3], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 4, 1, 5], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 5, 2, 4, 3], [1, 1, 1, 0]]} "Class ", 1385, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 4, 1, 5], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 2, 4, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 2, 5, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 4, 2, 3], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 4, 1, 5], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[1, 5, 2, 4, 3], [0, 0, 1, 1]]} "Class ", 1386, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 4, 1, 5], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 2, 4, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 2, 5, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 4, 2, 3], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 4, 1, 5], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[1, 5, 2, 4, 3], [1, 0, 1, 1]]} "Class ", 1387, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 4, 1, 5], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 2, 4, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 2, 5, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 4, 2, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 4, 1, 5], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 5, 2, 4, 3], [0, 1, 1, 1]]} "Class ", 1388, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 4, 1, 5], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 2, 4, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 2, 5, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 4, 2, 3], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 4, 1, 5], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 5, 2, 4, 3], [1, 1, 1, 1]]} "Class ", 1389, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 4, 5, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 2, 4, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 2, 1, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 4, 2, 3], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 4, 5, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 1, 2, 4, 3], [0, 0, 1, 0]]} "Class ", 1390, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 4, 5, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 2, 4, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 2, 1, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 4, 2, 3], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 4, 5, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 1, 2, 4, 3], [1, 0, 1, 0]]} "Class ", 1391, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 4, 5, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 2, 4, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 2, 1, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 4, 2, 3], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 4, 5, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 1, 2, 4, 3], [0, 1, 1, 0]]} "Class ", 1392, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 4, 5, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 2, 4, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 2, 1, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 4, 2, 3], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 4, 5, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 1, 2, 4, 3], [1, 1, 1, 0]]} "Class ", 1393, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 4, 5, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 2, 4, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 2, 1, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 4, 2, 3], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 4, 5, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 1, 2, 4, 3], [0, 0, 1, 1]]} "Class ", 1394, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 4, 5, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 2, 4, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 2, 1, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 4, 2, 3], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 4, 5, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 1, 2, 4, 3], [1, 0, 1, 1]]} "Class ", 1395, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 4, 5, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 2, 4, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 2, 1, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 4, 2, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 4, 5, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 1, 2, 4, 3], [0, 1, 1, 1]]} "Class ", 1396, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 4, 5, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 2, 4, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 2, 1, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 4, 2, 3], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 4, 5, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 1, 2, 4, 3], [1, 1, 1, 1]]} "Class ", 1397, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 1, 4], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 1, 4, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 5, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 5, 2, 3], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 5, 1, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 1, 4], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 1, 4, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 5, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 5, 2, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 2, 5, 1, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 3, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 832, 3856, 19332, 104100, 598191, 3649207, 23530003, 159758418, 1138377801, 8488557135, 66068553443, 535523151446, 4511235715048, 39422594627858] "" "Class ", 1398, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 1, 4], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 1, 4, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 5, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 5, 2, 3], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 5, 1, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 1, 4], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 1, 4, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 5, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 5, 2, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 2, 5, 1, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 823, 3790, 18858, 100681, 573288, 3463908, 22113021, 148597878, 1047753478, 7729545148, 59511864692, 477125552451, 3975258703984, 34356621400216] "" "Class ", 1399, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 1, 4], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 1, 4, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 5, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 5, 2, 3], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 5, 1, 4], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 5, 1, 4, 3], [0, 1, 0, 0]]} "Class ", 1400, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 1, 4], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 1, 4, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 5, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 5, 2, 3], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 5, 1, 4], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 5, 1, 4, 3], [1, 1, 0, 0]]} "Class ", 1401, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 1, 4], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 1, 4, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 5, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 5, 2, 3], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 5, 1, 4], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 5, 1, 4, 3], [0, 0, 1, 0]]} "Class ", 1402, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 1, 4], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 1, 4, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 5, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 5, 2, 3], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 5, 1, 4], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[2, 5, 1, 4, 3], [1, 0, 1, 0]]} "Class ", 1403, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 1, 4], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 1, 4, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 5, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 5, 2, 3], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 5, 1, 4], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 5, 1, 4, 3], [0, 1, 1, 0]]} "Class ", 1404, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 1, 4], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 1, 4, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 5, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 5, 2, 3], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 5, 1, 4], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 5, 1, 4, 3], [1, 1, 1, 0]]} "Class ", 1405, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 1, 4], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 1, 4, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 5, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 5, 2, 3], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 5, 1, 4], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 5, 1, 4, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 1, 4], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 1, 4, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 5, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 5, 2, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 5, 1, 4, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 822, 3770, 18673, 99202, 561850, 3376474, 21443619, 143403730, 1006668355, 7397305072, 56760081744, 453757775715, 3771725949468, 32538299983299] "" "Class ", 1406, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 1, 4], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 1, 4, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 5, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 5, 2, 3], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 5, 1, 4], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[2, 5, 1, 4, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 1, 4], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 1, 4, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 5, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 5, 2, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 5, 1, 4, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 812, 3691, 18068, 94650, 527672, 3116144, 19418534, 127269101, 874706366, 6287886812, 47167578100, 368443840717, 2991325251789, 25198172557339] "" "Class ", 1407, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 1, 4], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 1, 4, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 5, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 5, 2, 3], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 5, 1, 4], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 5, 1, 4, 3], [0, 1, 0, 1]]} "Class ", 1408, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 1, 4], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 1, 4, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 5, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 5, 2, 3], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 5, 1, 4], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 5, 1, 4, 3], [1, 1, 0, 1]]} "Class ", 1409, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 1, 4], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 1, 4, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 5, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 5, 2, 3], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 5, 1, 4], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 5, 1, 4, 3], [0, 0, 1, 1]]} "Class ", 1410, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 1, 4], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 1, 4, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 5, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 5, 2, 3], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 5, 1, 4], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[2, 5, 1, 4, 3], [1, 0, 1, 1]]} "Class ", 1411, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 1, 4], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 1, 4, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 5, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 5, 2, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 5, 1, 4], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 5, 1, 4, 3], [0, 1, 1, 1]]} "Class ", 1412, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 1, 4], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 1, 4, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 5, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 5, 2, 3], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 5, 1, 4], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 5, 1, 4, 3], [1, 1, 1, 1]]} "Class ", 1413, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 4, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 1, 4, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 2, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 5, 2, 3], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 5, 4, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 4, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 1, 4, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 2, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 5, 2, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 2, 5, 4, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [ [2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}] , [[2, 1, 5, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 1, 5, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 2, 5, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 828, 3841, 19275, 103804, 596238, 3634214, 23401721, 158590510, 1127386347, 8382833113, 65033007102, 525198055293, 4406373335727, 38336982246173] "" "Class ", 1414, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 4, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 1, 4, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 2, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 5, 2, 3], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 5, 4, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 4, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 1, 4, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 2, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 5, 2, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 2, 5, 4, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 789, 3498, 16593, 83664, 445971, 2502030, 14718189, 90486387, 579774807, 3862014909, 26687220198, 190936039110, 1411937246232, 10774765224822] "" "Class ", 1415, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 4, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 1, 4, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 2, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 5, 2, 3], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 5, 4, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 2, 1, 4, 3], [0, 1, 0, 0]]} "Class ", 1416, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 4, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 1, 4, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 2, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 5, 2, 3], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 5, 4, 1], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 2, 1, 4, 3], [1, 1, 0, 0]]} "Class ", 1417, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 4, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 1, 4, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 2, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 5, 2, 3], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 5, 4, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 2, 1, 4, 3], [0, 0, 1, 0]]} "Class ", 1418, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 4, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 1, 4, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 2, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 5, 2, 3], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 5, 4, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 2, 1, 4, 3], [1, 0, 1, 0]]} "Class ", 1419, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 4, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 1, 4, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 2, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 5, 2, 3], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 5, 4, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 2, 1, 4, 3], [0, 1, 1, 0]]} "Class ", 1420, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 4, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 1, 4, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 2, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 5, 2, 3], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 5, 4, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 2, 1, 4, 3], [1, 1, 1, 0]]} "Class ", 1421, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 4, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 1, 4, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 2, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 5, 2, 3], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 5, 4, 1], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 2, 1, 4, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 4, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 1, 4, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 2, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 5, 2, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 2, 1, 4, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {[0, 0, 1, 0, 0]}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 815, 3732, 18443, 97625, 550370, 3288509, 20737426, 137511671, 955865461, 6946143073, 52641758235, 415161323552, 3400630000892, 28879973055369] "" "Class ", 1422, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 4, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 1, 4, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 2, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 5, 2, 3], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 5, 4, 1], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 2, 1, 4, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 4, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 1, 4, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 2, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 5, 2, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 2, 1, 4, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {3}, {}], [[4, 2, 1, 3], {2}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 773, 3337, 15226, 72937, 364960, 1900116, 10261513, 57340073, 330851623, 1967865896, 12048036823, 75832308455, 490158666371, 3250462236986] "" "Class ", 1423, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 4, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 1, 4, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 2, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 5, 2, 3], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 5, 4, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 2, 1, 4, 3], [0, 1, 0, 1]]} "Class ", 1424, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 4, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 1, 4, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 2, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 5, 2, 3], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 5, 4, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 2, 1, 4, 3], [1, 1, 0, 1]]} "Class ", 1425, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 4, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 1, 4, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 2, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 5, 2, 3], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 5, 4, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 2, 1, 4, 3], [0, 0, 1, 1]]} "Class ", 1426, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 4, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 1, 4, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 2, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 5, 2, 3], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 5, 4, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 2, 1, 4, 3], [1, 0, 1, 1]]} "Class ", 1427, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 4, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 1, 4, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 2, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 5, 2, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 5, 4, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 2, 1, 4, 3], [0, 1, 1, 1]]} "Class ", 1428, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 5, 4, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 1, 4, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 4, 1, 2, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 5, 2, 3], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 5, 4, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 2, 1, 4, 3], [1, 1, 1, 1]]} "Class ", 1429, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 1, 2, 5], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 5, 2, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 5, 4, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 1, 4, 3], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 1, 2, 5], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 4, 5, 2, 3], [0, 1, 0, 1]]} "Class ", 1430, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 1, 2, 5], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 5, 2, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 5, 4, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 1, 4, 3], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 1, 2, 5], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 4, 5, 2, 3], [1, 1, 0, 1]]} "Class ", 1431, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 1, 2, 5], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 5, 2, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 5, 4, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 1, 4, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 1, 2, 5], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 4, 5, 2, 3], [0, 1, 1, 1]]} "Class ", 1432, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 1, 2, 5], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 5, 2, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 5, 4, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 1, 4, 3], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 1, 2, 5], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 4, 5, 2, 3], [1, 1, 1, 1]]} "Class ", 1433, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 1, 5, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 5, 2, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 5, 1, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 1, 4, 3], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 1, 5, 2], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 1, 5, 2, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 4, 1, 5, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 5, 2, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 5, 1, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 1, 4, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[4, 1, 5, 2, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 3}, {}], [[3, 1, 4, 2], {1, 3}, {[0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 864, 4022, 20194, 108560, 621126, 3763625, 24051735, 161530319, 1136544577, 8355391608, 64025836164, 510300177642, 4222282256130, 36205092814900] "" "Class ", 1434, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 1, 5, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 5, 2, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 5, 1, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 1, 4, 3], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 1, 5, 2], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 1, 5, 2, 3], [1, 0, 0, 1]]} "Class ", 1435, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 1, 5, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 5, 2, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 5, 1, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 1, 4, 3], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 1, 5, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 1, 5, 2, 3], [0, 1, 0, 1]]} "Class ", 1436, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 1, 5, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 5, 2, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 5, 1, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 1, 4, 3], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 1, 5, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 1, 5, 2, 3], [1, 1, 0, 1]]} "Class ", 1437, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 1, 5, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 5, 2, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 5, 1, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 1, 4, 3], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 1, 5, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 1, 5, 2, 3], [0, 0, 1, 1]]} "Class ", 1438, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 1, 5, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 5, 2, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 5, 1, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 1, 4, 3], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 1, 5, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 1, 5, 2, 3], [1, 0, 1, 1]]} "Class ", 1439, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 1, 5, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 5, 2, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 5, 1, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 1, 4, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 1, 5, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 1, 5, 2, 3], [0, 1, 1, 1]]} "Class ", 1440, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 1, 5, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 5, 2, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 5, 1, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 1, 4, 3], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 1, 5, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 1, 5, 2, 3], [1, 1, 1, 1]]} "Class ", 1441, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 2, 1, 5], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 4, 2, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 4, 5, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 2, 4, 3], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 2, 1, 5], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[1, 5, 4, 2, 3], [0, 0, 0, 1]]} "Class ", 1442, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 2, 1, 5], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 4, 5, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 2, 4, 3], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 2, 1, 5], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 4, 2, 1, 5], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 4, 5, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 2, 4, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 863, 4001, 19917, 105594, 592404, 3498355, 21650945, 139914802, 941163116, 6572178283, 47531160988, 355285488652, 2739772751897, 21761249515981] "" "Class ", 1443, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 2, 1, 5], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 4, 2, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 4, 5, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 2, 4, 3], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 2, 1, 5], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 5, 4, 2, 3], [0, 1, 0, 1]]} "Class ", 1444, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 2, 1, 5], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 4, 2, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 4, 5, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 2, 4, 3], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 2, 1, 5], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 5, 4, 2, 3], [1, 1, 0, 1]]} "Class ", 1445, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 2, 1, 5], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 4, 2, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 4, 5, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 2, 4, 3], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 2, 1, 5], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[1, 5, 4, 2, 3], [0, 0, 1, 1]]} "Class ", 1446, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 2, 1, 5], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 4, 2, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 4, 5, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 2, 4, 3], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 2, 1, 5], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[1, 5, 4, 2, 3], [1, 0, 1, 1]]} "Class ", 1447, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 2, 1, 5], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 4, 2, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 4, 5, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 2, 4, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 2, 1, 5], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 5, 4, 2, 3], [0, 1, 1, 1]]} "Class ", 1448, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 2, 1, 5], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 4, 2, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 4, 5, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 2, 4, 3], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 2, 1, 5], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 5, 4, 2, 3], [1, 1, 1, 1]]} "Class ", 1449, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 2, 5, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 4, 2, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 4, 1, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 2, 4, 3], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 2, 5, 1], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 1, 4, 2, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 4, 2, 5, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 4, 2, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 4, 1, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 2, 4, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 1, 4, 2, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 3}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 864, 4026, 20257, 109237, 627540, 3821562, 24566373, 166098061, 1177446965, 8727119151, 67466899214, 542816230810, 4536340922899, 39307939237185] "" "Class ", 1450, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 2, 5, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 4, 2, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 4, 1, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 2, 4, 3], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 2, 5, 1], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 1, 4, 2, 3], [1, 0, 0, 1]]} "Class ", 1451, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 2, 5, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 4, 2, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 4, 1, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 2, 4, 3], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 2, 5, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 1, 4, 2, 3], [0, 1, 0, 1]]} "Class ", 1452, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 2, 5, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 4, 2, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 4, 1, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 2, 4, 3], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 2, 5, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 1, 4, 2, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 4, 2, 5, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 4, 2, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 4, 1, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 2, 4, 3], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 1, 4, 2, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {}, {}], [[3, 2, 4, 1], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {3}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {4}, {}], [[3, 1, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 5, 4, 2], {4}, {}], [[3, 2, 5, 4, 1], {1, 2, 4}, {}], [[4, 1, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 5, 3, 2], {4}, {[0, 0, 1, 0, 0, 0]}], [[4, 2, 5, 3, 1], {1, 2, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 859, 3931, 19119, 97921, 524460, 2921730, 16858380, 100405010, 615519965, 3874925015, 25001381089, 165049371943, 1113222988121, 7661588927073] "" "Class ", 1453, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 2, 5, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 4, 2, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 4, 1, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 2, 4, 3], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 2, 5, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 1, 4, 2, 3], [0, 0, 1, 1]]} "Class ", 1454, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 2, 5, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 4, 2, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 4, 1, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 2, 4, 3], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 2, 5, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 1, 4, 2, 3], [1, 0, 1, 1]]} "Class ", 1455, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 2, 5, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 4, 2, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 4, 1, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 2, 4, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 2, 5, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 1, 4, 2, 3], [0, 1, 1, 1]]} "Class ", 1456, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 2, 5, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 4, 2, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 4, 1, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 2, 4, 3], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 2, 5, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 1, 4, 2, 3], [1, 1, 1, 1]]} "Class ", 1457, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 5, 1, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 1, 5, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 5, 4, 3], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 5, 1, 2], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 4, 5, 1, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 1, 5, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 5, 4, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 867, 4067, 20653, 112654, 655857, 4053944, 26485349, 182188710, 1315150820, 9933427039, 78301800658, 642683095064, 5481281053460, 48486794797019] "" "Class ", 1458, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 5, 1, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 1, 2, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 1, 5, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 5, 4, 3], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 5, 1, 2], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 5, 1, 2, 3], [1, 0, 0, 1]]} "Class ", 1459, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 1, 5, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]} "Class ", 1460, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 5, 1, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 1, 2, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 1, 5, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 5, 4, 3], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 5, 1, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 5, 1, 2, 3], [1, 1, 0, 1]]} "Class ", 1461, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 5, 1, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 1, 2, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 1, 5, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 5, 4, 3], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 5, 1, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 5, 1, 2, 3], [0, 0, 1, 1]]} "Class ", 1462, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 5, 1, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 1, 2, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 1, 5, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 5, 4, 3], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 5, 1, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 5, 1, 2, 3], [1, 0, 1, 1]]} "Class ", 1463, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 5, 1, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 1, 5, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 5, 4, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 5, 1, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 4, 5, 1, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 1, 5, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 5, 4, 3], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {[0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {4}, {}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {4}, {}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {4}, {[0, 0, 1, 0, 0, 0]}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {4}, {[0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 4, 1], {2, 3}, {}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3, 4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 860, 3952, 19397, 100929, 553729, 3189991, 19234719, 121069949, 793718495, 5409112057, 38252200820, 280266354718, 2124422696960, 16637455794172] "" "Class ", 1464, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 5, 1, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 1, 2, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 1, 5, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 5, 4, 3], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 5, 1, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 5, 1, 2, 3], [1, 1, 1, 1]]} "Class ", 1465, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 5, 2, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 1, 4, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 5, 4, 3], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 5, 2, 1], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 4, 5, 2, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 1, 4, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 5, 4, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {[0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 864, 4026, 20257, 109237, 627540, 3821562, 24566373, 166098061, 1177446965, 8727119151, 67466899214, 542816230810, 4536340922899, 39307939237185] "" "Class ", 1466, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 5, 2, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 1, 4, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 5, 2, 1], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 4, 5, 2, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 1, 4, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {3}, {}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {[0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 861, 3981, 19805, 105308, 595248, 3560848, 22458802, 148857252, 1033834557, 7504498075, 56805746800, 447478430120, 3661460393157, 31067368943539] "" "Class ", 1467, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 5, 2, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 5, 2, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]} "Class ", 1468, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 5, 2, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 5, 2, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]} "Class ", 1469, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 5, 2, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 1, 2, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 1, 4, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 5, 4, 3], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 5, 2, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 4, 1, 2, 3], [0, 0, 1, 1]]} "Class ", 1470, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 5, 2, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 1, 2, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 1, 4, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 5, 4, 3], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 5, 2, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 4, 1, 2, 3], [1, 0, 1, 1]]} "Class ", 1471, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 5, 2, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 5, 4, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 5, 2, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]} "Class ", 1472, " is:" {{[[1, 2, 3], [0, 1]], [[3, 4, 5, 2, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 5, 4, 3], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 4, 5, 2, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]} "Class ", 1473, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 1, 2, 4], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 5, 1, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 5, 4, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 1, 5, 3], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 1, 2, 4], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 4, 5, 1, 3], [0, 1, 0, 0]]} "Class ", 1474, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 1, 2, 4], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 5, 1, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 5, 4, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 1, 5, 3], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 1, 2, 4], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 4, 5, 1, 3], [1, 1, 0, 0]]} "Class ", 1475, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 1, 2, 4], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 5, 1, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 5, 4, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 1, 5, 3], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 1, 2, 4], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 4, 5, 1, 3], [0, 1, 1, 0]]} "Class ", 1476, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 1, 2, 4], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 5, 1, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 5, 4, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 1, 5, 3], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 1, 2, 4], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 4, 5, 1, 3], [1, 1, 1, 0]]} "Class ", 1477, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 1, 2, 4], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 5, 1, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 5, 4, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 1, 5, 3], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 1, 2, 4], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 4, 5, 1, 3], [0, 1, 0, 1]]} "Class ", 1478, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 1, 2, 4], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 5, 1, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 5, 4, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 1, 5, 3], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 1, 2, 4], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 4, 5, 1, 3], [1, 1, 0, 1]]} "Class ", 1479, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 1, 2, 4], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 5, 1, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 5, 4, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 1, 5, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 1, 2, 4], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 4, 5, 1, 3], [0, 1, 1, 1]]} "Class ", 1480, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 1, 2, 4], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 5, 1, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 5, 4, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 1, 5, 3], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 1, 2, 4], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 4, 5, 1, 3], [1, 1, 1, 1]]} "Class ", 1481, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 5, 2, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 5, 3], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 5, 2, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 5, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 835, 3892, 19657, 106697, 618356, 3805911, 24765265, 169708660, 1220620805, 9187454157, 72180509333, 590544942586, 5021081153243, 44283817316156] "" "Class ", 1482, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 1, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 5, 2, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 5, 3], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 1, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 5, 2, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 5, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}] , [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 816, 3747, 18617, 99362, 566106, 3425275, 21913180, 147663716, 1044628461, 7735819689, 59811961455, 481735814205, 4033420581463, 35040772359300] "" "Class ", 1483, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 1, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 5, 2, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 5, 3], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 2, 5, 1, 3], [0, 1, 0, 0]]} "Class ", 1484, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 1, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 5, 2, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 5, 3], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 1, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 5, 2, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 5, 3], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}] , [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [ [4, 5, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 5, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 5, 3, 2, 1], {4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 804, 3646, 17845, 93644, 523900, 3109648, 19501471, 128752376, 892078074, 6468403288, 48961942463, 386029724594, 3163823869930, 26905707777479] "" "Class ", 1485, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 1, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 5, 2, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 5, 3], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 2, 5, 1, 3], [0, 0, 1, 0]]} "Class ", 1486, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 1, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 5, 2, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 5, 3], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 2, 5, 1, 3], [1, 0, 1, 0]]} "Class ", 1487, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 1, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 5, 2, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 5, 3], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 2, 5, 1, 3], [0, 1, 1, 0]]} "Class ", 1488, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 1, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 5, 2, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 5, 3], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 2, 5, 1, 3], [1, 1, 1, 0]]} "Class ", 1489, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 5, 2, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 5, 3], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 5, 2, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 5, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 3}, {}], [[3, 1, 4, 2], {1, 3}, {}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 803, 3631, 17695, 92332, 513037, 3021517, 18787232, 122906066, 843430989, 6055260684, 45372050492, 354067350521, 2871995419977, 24172238255557] "" "Class ", 1490, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 1, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 5, 2, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 5, 3], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 2, 5, 1, 3], [1, 0, 0, 1]]} "Class ", 1491, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 1, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 5, 2, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 5, 3], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 2, 5, 1, 3], [0, 1, 0, 1]]} "Class ", 1492, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 1, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 5, 2, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 5, 3], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 2, 5, 1, 3], [1, 1, 0, 1]]} "Class ", 1493, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 1, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 5, 2, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 5, 3], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 2, 5, 1, 3], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 1, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 5, 2, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 5, 3], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[4, 2, 5, 1, 3], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {}], [[3, 1, 4, 2], {}, {}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 1, 0, 0]}], [[3, 1, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 5, 3, 2], {4}, {}], [[4, 2, 5, 3, 1], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 762, 3257, 14741, 70307, 351984, 1843397, 10068830, 57206764, 337290995, 2059458851, 12998678963, 84671718397, 568381956482, 3926785095367] "" "Class ", 1494, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 1, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 5, 2, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 5, 3], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 2, 5, 1, 3], [1, 0, 1, 1]]} "Class ", 1495, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 1, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 5, 2, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 5, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 2, 5, 1, 3], [0, 1, 1, 1]]} "Class ", 1496, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 1, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 5, 2, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 5, 3], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 1, 4, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 2, 5, 1, 3], [1, 1, 1, 1]]} "Class ", 1497, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 1, 4], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 1, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 5, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 5, 3], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 2, 1, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 1, 4], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 1, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 5, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 5, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 5, 2, 1, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 5, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 5, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 832, 3859, 19357, 104293, 599637, 3660135, 23613100, 160405728, 1143560661, 8531290194, 66431591492, 538702633134, 4539935555717, 39689480449999] "" "Class ", 1498, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 1, 4], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 1, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 5, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 5, 3], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 2, 1, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 1, 4], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 1, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 5, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 5, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 5, 2, 1, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 823, 3790, 18858, 100681, 573288, 3463908, 22113021, 148597878, 1047753478, 7729545148, 59511864692, 477125552451, 3975258703984, 34356621400216] "" "Class ", 1499, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 1, 4], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 1, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 5, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 5, 3], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 2, 1, 4], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 5, 4, 1, 3], [0, 1, 0, 0]]} "Class ", 1500, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 1, 4], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 1, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 5, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 5, 3], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 2, 1, 4], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 5, 4, 1, 3], [1, 1, 0, 0]]} "Class ", 1501, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 1, 4], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 1, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 5, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 5, 3], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 2, 1, 4], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 5, 4, 1, 3], [0, 0, 1, 0]]} "Class ", 1502, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 1, 4], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 1, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 5, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 5, 3], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 2, 1, 4], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[2, 5, 4, 1, 3], [1, 0, 1, 0]]} "Class ", 1503, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 1, 4], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 1, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 5, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 5, 3], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 2, 1, 4], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 5, 4, 1, 3], [0, 1, 1, 0]]} "Class ", 1504, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 1, 4], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 1, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 5, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 5, 3], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 2, 1, 4], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 5, 4, 1, 3], [1, 1, 1, 0]]} "Class ", 1505, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 1, 4], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 1, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 5, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 5, 3], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 2, 1, 4], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 5, 4, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 1, 4], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 1, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 5, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 5, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 5, 4, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 799, 3582, 17238, 88493, 482074, 2775237, 16823508, 107064936, 713395543, 4965291679, 36022440846, 271887675081, 2131279620476, 17323532892062] "" "Class ", 1506, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 1, 4], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 1, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 5, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 5, 3], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 2, 1, 4], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[2, 5, 4, 1, 3], [1, 0, 0, 1]]} "Class ", 1507, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 1, 4], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 1, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 5, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 5, 3], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 2, 1, 4], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 5, 4, 1, 3], [0, 1, 0, 1]]} "Class ", 1508, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 1, 4], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 1, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 5, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 5, 3], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 2, 1, 4], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 5, 4, 1, 3], [1, 1, 0, 1]]} "Class ", 1509, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 1, 4], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 1, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 5, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 5, 3], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 2, 1, 4], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 5, 4, 1, 3], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 1, 4], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 1, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 5, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 5, 3], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 5, 4, 1, 3], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {4}, {}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 773, 3336, 15207, 72697, 362447, 1876392, 10051083, 55544661, 315899245, 1845139684, 11048651523, 67719859612, 424287619507, 2714074517843] "" "Class ", 1510, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 1, 4], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 1, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 5, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 5, 3], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 2, 1, 4], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[2, 5, 4, 1, 3], [1, 0, 1, 1]]} "Class ", 1511, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 1, 4], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 1, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 5, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 5, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 2, 1, 4], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 5, 4, 1, 3], [0, 1, 1, 1]]} "Class ", 1512, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 1, 4], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 1, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 5, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 5, 3], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 2, 1, 4], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 5, 4, 1, 3], [1, 1, 1, 1]]} "Class ", 1513, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 2, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 5, 3], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 2, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 5, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 5, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 840, 3936, 19957, 108727, 632418, 3906036, 25500430, 175290097, 1264494280, 9544528131, 75187715874, 616731611679, 5256655964668, 46471089949493] "" "Class ", 1514, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 2, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 5, 3], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 2, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 5, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 817, 3757, 18687, 99832, 569281, 3447064, 22066989, 148785990, 1053102759, 7802083427, 60348477824, 486231231347, 4072369843780, 35389420714032] "" "Class ", 1515, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 2, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 5, 3], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [0, 1, 0, 0]]} "Class ", 1516, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 2, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 5, 3], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 2, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 5, 3], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 5, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 5, 3, 2, 1], {4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 794, 3575, 17370, 90465, 502361, 2960475, 18438046, 120926064, 832555209, 6000411082, 45158489989, 354091882583, 2886914319531, 24428575330008] "" "Class ", 1517, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 2, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 5, 3], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [0, 0, 1, 0]]} "Class ", 1518, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 2, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 5, 3], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [1, 0, 1, 0]]} "Class ", 1519, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 2, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 5, 3], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [0, 1, 1, 0]]} "Class ", 1520, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 2, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 5, 3], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [1, 1, 1, 0]]} "Class ", 1521, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 2, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 5, 3], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 2, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 5, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 3}, {}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 807, 3683, 18163, 96125, 542802, 3254078, 20623128, 137666728, 964832024, 7079248143, 54242139425, 433028551769, 3594508078816, 30967247808068] "" "Class ", 1522, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 2, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 5, 3], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 2, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 5, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 3, 2], {3}, {}], [[5, 2, 4, 3, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 779, 3431, 16199, 81557, 436188, 2469808, 14760224, 92848108, 613228596, 4242552264, 30678533107, 231395807183, 1817022923630, 14827716336496] "" "Class ", 1523, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 2, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 5, 3], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [0, 1, 0, 1]]} "Class ", 1524, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 2, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 5, 3], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [1, 1, 0, 1]]} "Class ", 1525, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 2, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 5, 3], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 2, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 5, 3], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 3, 2], {4}, {}], [[5, 2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 781, 3465, 16557, 84664, 461013, 2662032, 16239307, 104311522, 703458972, 4967651815, 36647105250, 281817953785, 2254684875973, 18733173560004] "" "Class ", 1526, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 2, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 5, 3], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [1, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 2, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 5, 3], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 3, 2], {4}, {}], [[5, 2, 4, 3, 1], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 747, 3110, 13532, 61202, 286606, 1385818, 6904771, 35397468, 186508447, 1009179949, 5604102933, 31922266494, 186446899551, 1116196669984] "" "Class ", 1527, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 2, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 5, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [0, 1, 1, 1]]} "Class ", 1528, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 4, 2, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 5, 3], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 2, 4, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 2, 4, 1, 3], [1, 1, 1, 1]]} "Class ", 1529, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 5, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 5, 3], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 5, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 5, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [2, 5, 4, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 198, 853, 4019, 20496, 112282, 656429, 4073541, 26712196, 184387711, 1335348860, 10116618462, 79972464650, 658143165349, 5627158883123, 49894085513898] "" "Class ", 1530, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 5, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 5, 3], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 5, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 5, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 822, 3775, 18708, 99362, 562245, 3372683, 21356544, 142241471, 993342219, 7253513734, 55247151937, 437959067272, 3606339486556, 30792044130007] "" "Class ", 1531, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 5, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 0, 1, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 5, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {1, 2}, %1], [[1, 5, 3, 4, 2], {2, 3}, %1], [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 3, 1, 4], {3, 4}, %1], [[2, 5, 3, 4, 1], {3}, %1], [ [2, 5, 4, 1, 3], {2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 4, 2, 1], {4}, {[0, 0, 0, 0, 0, 1]}]} %1 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 813, 3712, 18303, 96776, 545471, 3261061, 20591121, 136818580, 953607801, 6952421005, 52888794641, 418878582936, 3447013846331, 29420183713185] "" "Class ", 1532, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 5, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 5, 3], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 5, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 5, 3], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 3, 1, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [ [2, 5, 3, 4, 1], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [ [2, 5, 4, 1, 3], {2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 4, 2, 1], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 786, 3460, 16247, 80880, 424710, 2342567, 13523299, 81457720, 510610460, 3323145937, 22409073519, 156287130686, 1125483716903, 8356669563214] "" "Class ", 1533, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 5, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 5, 3], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [0, 0, 1, 0]]} "Class ", 1534, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 5, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 5, 3], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [1, 0, 1, 0]]} "Class ", 1535, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 5, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 5, 3], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 1, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 5, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 5, 3], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {4}, {}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {4}, {}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {4}, {}], [[3, 4, 2, 1, 5], {3}, {}], [[3, 4, 2, 5, 1], {4}, {}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {4}, {}], [[3, 5, 2, 1, 4], {3}, {}], [[3, 5, 2, 4, 1], {4}, {}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {4}, {}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {4}, {}], [[4, 5, 3, 1, 2], {3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 781, 3469, 16631, 85491, 468537, 2724833, 16747171, 108389911, 736382213, 5236791237, 38885666991, 300817541531, 2419516810609, 20196271982281] "" "Class ", 1536, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 5, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 5, 3], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [1, 1, 1, 0]]} "Class ", 1537, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 5, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 5, 3], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 5, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 5, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 826, 3826, 19192, 103460, 595619, 3642546, 23557040, 160483907, 1147825394, 8593549583, 67172163192, 546912678465, 4628661844716, 40643206332458] "" "Class ", 1538, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 5, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 5, 3], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [1, 0, 0, 1]]} "Class ", 1539, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 5, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 5, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {4}, {}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {4}, {}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {4}, {}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {4}, {}], [[3, 5, 2, 4, 1], {2, 3}, {}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {4}, {[0, 0, 0, 1, 0, 0]}], [[4, 5, 2, 3, 1], {3, 4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 787, 3474, 16385, 82086, 434787, 2425495, 14204293, 87075908, 557370385, 3716917695, 25771442227, 185446213578, 1382608160683, 10664068755489] "" "Class ", 1540, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 5, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 5, 3], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [1, 1, 0, 1]]} "Class ", 1541, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 5, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 5, 3], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [0, 0, 1, 1]]} "Class ", 1542, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 5, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 5, 3], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [1, 0, 1, 1]]} "Class ", 1543, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 5, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 5, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 5, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 5, 3], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {4}, {}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {4}, {}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {4}, {}], [[3, 4, 2, 5, 1], {1, 2}, {[0, 0, 1, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {4}, {}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 1, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {4}, {[0, 0, 0, 1, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 749, 3149, 13997, 65637, 324093, 1681557, 9148685, 52083509, 309639629, 1918634805, 12368650701, 82815657525, 575014148813, 4134126910517] "" "Class ", 1544, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 5, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 5, 3], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 4, 1, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 5, 2, 1, 3], [1, 1, 1, 1]]} "Class ", 1545, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 4, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 4, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [2, 5, 4, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [3, 5, 4, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 828, 3840, 19263, 103707, 595495, 3628516, 23357134, 158232925, 1124446784, 8357996972, 64817032778, 523264497910, 4388556318724, 38168084582544] "" "Class ", 1546, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 4, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 4, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 799, 3630, 17827, 93842, 526424, 3132120, 19683089, 130160755, 902809435, 6549810352, 49580278628, 390730952741, 3199414514124, 27171039245421] "" "Class ", 1547, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 4, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 0, 1, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 4, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {1, 2}, %1], [[1, 5, 3, 4, 2], {2, 3}, %1], [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 3, 1, 4], {3, 4}, %1], [[2, 5, 3, 4, 1], {3}, %1], [ [2, 5, 4, 1, 3], {2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [3, 5, 4, 1, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} %1 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 783, 3466, 16471, 83447, 448428, 2544454, 15186808, 95034029, 621711025, 4241298889, 30104874430, 221886988862, 1695120017724, 13400890574172] "" "Class ", 1548, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 1, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 4, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 5, 3], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 1, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 4, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 5, 3], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 3, 1, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0]}], [ [2, 5, 3, 4, 1], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0]}], [ [2, 5, 4, 1, 3], {2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 5, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 760, 3280, 15096, 73656, 379135, 2050329, 11608472, 68602785, 422073206, 2697209051, 17866377069, 122450956944, 866922897764, 6330653919980] "" "Class ", 1549, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 1, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 4, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 5, 3], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 4, 2, 1, 3], [0, 0, 1, 0]]} "Class ", 1550, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 1, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 4, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 5, 3], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 4, 2, 1, 3], [1, 0, 1, 0]]} "Class ", 1551, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 1, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 4, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 5, 3], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 4, 2, 1, 3], [0, 1, 1, 0]]} "Class ", 1552, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 1, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 4, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 5, 3], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 4, 2, 1, 3], [1, 1, 1, 0]]} "Class ", 1553, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 4, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 4, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {[0, 0, 0, 1, 0, 0]}], [[2, 5, 4, 3, 1], {1, 2}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 792, 3535, 16914, 86166, 464497, 2636341, 15689680, 97557827, 631845006, 4251208396, 29645060247, 213813263409, 1592082305098, 12218890953967] "" "Class ", 1554, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 4, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 4, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {3}, {[0, 0, 0, 1, 0, 0]}], [[2, 5, 4, 3, 1], {1, 3}, {[0, 0, 0, 1, 0, 0]}], [[4, 1, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 3, 2], {3}, {[0, 0, 0, 1, 0, 0]}], [[5, 2, 4, 3, 1], {2, 3}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 753, 3191, 14264, 66837, 326622, 1657807, 8709763, 47231022, 263725171, 1513156426, 8905320748, 53675059400, 330869939739, 2083414782811] "" "Class ", 1555, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 4, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 4, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 1, 4], {}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 1, 3], {}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {1}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {[0, 0, 0, 1, 0, 0]}], [[2, 5, 4, 3, 1], {1, 2}, {[0, 0, 0, 1, 0, 0]}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2}, {}], [[4, 2, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {1, 2}, {}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {4}, {}], [[4, 3, 2, 5, 1], {3, 4}, {}], [[5, 2, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2}, {}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {4}, {}], [[5, 3, 2, 4, 1], {3, 4}, {}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {4}, {[0, 0, 0, 1, 0, 0]}], [[5, 4, 2, 3, 1], {1, 3}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 751, 3155, 13897, 63782, 303621, 1493661, 7571874, 39458863, 210960190, 1155105367, 6467821833, 36986263206, 215757243633, 1282579464962] "" "Class ", 1556, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 4, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]} "Class ", 1557, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 1, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 4, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 5, 3], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 4, 2, 1, 3], [0, 0, 1, 1]]} "Class ", 1558, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 1, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 4, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 5, 3], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 4, 2, 1, 3], [1, 0, 1, 1]]} "Class ", 1559, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 1, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 4, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 5, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 4, 2, 1, 3], [0, 1, 1, 1]]} "Class ", 1560, " is:" {{[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 1, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[3, 1, 2, 4, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 5, 3], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 5, 4, 2, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 4, 2, 1, 3], [1, 1, 1, 1]]} "Class ", 1561, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 2, 3, 5], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 4, 5, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 4, 3, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 3, 2, 1, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 2, 3, 5], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 3, 4, 5, 2], [0, 1, 1, 0]]} "Class ", 1562, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 2, 3, 5], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 4, 5, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 4, 3, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 3, 2, 1, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 2, 3, 5], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 3, 4, 5, 2], [1, 1, 1, 0]]} "Class ", 1563, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 2, 3, 5], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 4, 5, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 4, 3, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 3, 2, 1, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 2, 3, 5], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 3, 4, 5, 2], [0, 1, 1, 1]]} "Class ", 1564, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 2, 3, 5], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 4, 5, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 4, 3, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 3, 2, 1, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 2, 3, 5], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 3, 4, 5, 2], [1, 1, 1, 1]]} "Class ", 1565, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 2, 5, 3], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 4, 5, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 4, 1, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 2, 1, 4], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 2, 5, 3], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 1, 4, 5, 2], [0, 0, 1, 0]]} "Class ", 1566, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 2, 5, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 4, 5, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 4, 1, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 2, 1, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 2, 5, 3], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[3, 1, 4, 5, 2], [1, 0, 1, 0]]} "Class ", 1567, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 2, 5, 3], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 4, 5, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 4, 1, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 2, 1, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 2, 5, 3], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 1, 4, 5, 2], [0, 1, 1, 0]]} "Class ", 1568, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 2, 5, 3], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 4, 5, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 4, 1, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 2, 1, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 2, 5, 3], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 1, 4, 5, 2], [1, 1, 1, 0]]} "Class ", 1569, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 2, 5, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 4, 5, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 4, 1, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 2, 1, 4], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 2, 5, 3], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 1, 4, 5, 2], [0, 0, 1, 1]]} "Class ", 1570, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 2, 5, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 4, 5, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 4, 1, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 2, 1, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 2, 5, 3], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[3, 1, 4, 5, 2], [1, 0, 1, 1]]} "Class ", 1571, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 2, 5, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 4, 5, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 4, 1, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 2, 1, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 2, 5, 3], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 1, 4, 5, 2], [0, 1, 1, 1]]} "Class ", 1572, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 2, 5, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 4, 5, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 4, 1, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 2, 1, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 2, 5, 3], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 1, 4, 5, 2], [1, 1, 1, 1]]} "Class ", 1573, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 3, 2, 5], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 3, 5, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 3, 4, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 3, 1, 4], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 3, 2, 5], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[1, 4, 3, 5, 2], [0, 0, 1, 0]]} "Class ", 1574, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 3, 2, 5], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 3, 5, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 3, 4, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 3, 1, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 3, 2, 5], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[1, 4, 3, 5, 2], [1, 0, 1, 0]]} "Class ", 1575, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 3, 2, 5], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 3, 5, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 3, 4, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 3, 1, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 3, 2, 5], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 4, 3, 5, 2], [0, 1, 1, 0]]} "Class ", 1576, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 3, 2, 5], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 3, 5, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 3, 4, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 3, 1, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 3, 2, 5], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 4, 3, 5, 2], [1, 1, 1, 0]]} "Class ", 1577, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 3, 2, 5], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 3, 5, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 3, 4, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 3, 1, 4], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 3, 2, 5], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[1, 4, 3, 5, 2], [0, 0, 1, 1]]} "Class ", 1578, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 3, 2, 5], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 3, 5, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 3, 4, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 3, 1, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 3, 2, 5], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[1, 4, 3, 5, 2], [1, 0, 1, 1]]} "Class ", 1579, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 3, 2, 5], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 3, 5, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 3, 4, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 3, 1, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 3, 2, 5], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 4, 3, 5, 2], [0, 1, 1, 1]]} "Class ", 1580, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 3, 2, 5], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 3, 5, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 3, 4, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 3, 1, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 3, 2, 5], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 4, 3, 5, 2], [1, 1, 1, 1]]} "Class ", 1581, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 3, 5, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 3, 5, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 3, 1, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 3, 1, 4], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 3, 5, 2], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 1, 3, 5, 2], [0, 0, 1, 0]]} "Class ", 1582, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 3, 5, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 3, 5, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 3, 1, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 3, 1, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 3, 5, 2], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 1, 3, 5, 2], [1, 0, 1, 0]]} "Class ", 1583, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 3, 5, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 3, 5, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 3, 1, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 3, 1, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 3, 5, 2], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 1, 3, 5, 2], [0, 1, 1, 0]]} "Class ", 1584, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 3, 5, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 3, 5, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 3, 1, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 3, 1, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 3, 5, 2], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 1, 3, 5, 2], [1, 1, 1, 0]]} "Class ", 1585, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 3, 5, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 3, 5, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 3, 1, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 3, 1, 4], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 3, 5, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 1, 3, 5, 2], [0, 0, 1, 1]]} "Class ", 1586, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 3, 5, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 3, 5, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 3, 1, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 3, 1, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 3, 5, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 1, 3, 5, 2], [1, 0, 1, 1]]} "Class ", 1587, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 3, 5, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 3, 5, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 3, 1, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 3, 1, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 3, 5, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 1, 3, 5, 2], [0, 1, 1, 1]]} "Class ", 1588, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 3, 5, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 3, 5, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 3, 1, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 3, 1, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 3, 5, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 1, 3, 5, 2], [1, 1, 1, 1]]} "Class ", 1589, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 5, 2, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 1, 5, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 1, 4, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 5, 2, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 1, 5, 2, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 1, 5, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 1, 4, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 1, 5, 2, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [ [3, 1, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}] , [[4, 1, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 5, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[4, 2, 5, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 198, 850, 3991, 20295, 110902, 646824, 4005415, 26215393, 180646378, 1306205116, 9881724641, 78013981469, 641260307188, 5476803337918, 48511899988525] "" "Class ", 1590, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 5, 2, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 1, 5, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 1, 4, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 5, 1, 4], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 5, 2, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 1, 5, 2, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 1, 5, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 1, 4, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 5, 1, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 1, 5, 2, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 822, 3776, 18718, 99445, 562893, 3377721, 21395837, 142552004, 995845879, 7274193198, 55422447455, 439485327846, 3619994280219, 30917584228699] "" "Class ", 1591, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 5, 2, 3], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 1, 5, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 1, 4, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 5, 1, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 5, 2, 3], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 4, 1, 5, 2], [0, 1, 0, 0]]} "Class ", 1592, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 5, 2, 3], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 1, 5, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 1, 4, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 5, 1, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 5, 2, 3], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 4, 1, 5, 2], [1, 1, 0, 0]]} "Class ", 1593, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 5, 2, 3], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 1, 5, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 1, 4, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 5, 1, 4], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 5, 2, 3], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 4, 1, 5, 2], [0, 0, 1, 0]]} "Class ", 1594, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 5, 2, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 1, 5, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 1, 4, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 5, 1, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 5, 2, 3], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[3, 4, 1, 5, 2], [1, 0, 1, 0]]} "Class ", 1595, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 5, 2, 3], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 1, 5, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 1, 4, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 5, 1, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 5, 2, 3], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 4, 1, 5, 2], [0, 1, 1, 0]]} "Class ", 1596, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 5, 2, 3], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 1, 5, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 1, 4, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 5, 1, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 5, 2, 3], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 4, 1, 5, 2], [1, 1, 1, 0]]} "Class ", 1597, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 5, 2, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 1, 5, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 1, 4, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 5, 2, 3], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 4, 1, 5, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 1, 5, 2, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 1, 5, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 1, 4, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[3, 4, 1, 5, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 823, 3788, 18844, 100590, 572670, 3459479, 22080321, 148346842, 1045743476, 7712799601, 59367166397, 475831342515, 3963297148733, 34242569136489] "" "Class ", 1598, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 5, 2, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 1, 5, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 1, 4, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 5, 1, 4], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 5, 2, 3], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[3, 4, 1, 5, 2], [1, 0, 0, 1]]} "Class ", 1599, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 5, 2, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 1, 5, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 1, 4, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 5, 1, 4], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 5, 2, 3], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 4, 1, 5, 2], [0, 1, 0, 1]]} "Class ", 1600, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 5, 2, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 1, 5, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 1, 4, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 5, 1, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 5, 2, 3], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 4, 1, 5, 2], [1, 1, 0, 1]]} "Class ", 1601, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 5, 2, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 1, 5, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 1, 4, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 5, 1, 4], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 5, 2, 3], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 4, 1, 5, 2], [0, 0, 1, 1]]} "Class ", 1602, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 5, 2, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 1, 5, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 1, 4, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 5, 1, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 5, 2, 3], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[3, 4, 1, 5, 2], [1, 0, 1, 1]]} "Class ", 1603, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 5, 2, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 1, 5, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 1, 4, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 5, 1, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 5, 2, 3], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 4, 1, 5, 2], [0, 1, 1, 1]]} "Class ", 1604, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 5, 2, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 1, 5, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 1, 4, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 5, 1, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 5, 2, 3], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 4, 1, 5, 2], [1, 1, 1, 1]]} "Class ", 1605, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 5, 3, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 1, 5, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 1, 3, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 5, 1, 4], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 5, 3, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 1, 5, 3, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 1, 5, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 1, 3, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 5, 1, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 1, 5, 3, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [ [3, 1, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}] , [[4, 1, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 1, 5, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 833, 3867, 19418, 104628, 601283, 3666429, 23617002, 160097114, 1138404153, 8466853429, 65699662209, 530691913390, 4453322485112, 38752402787455] "" "Class ", 1606, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 5, 3, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 1, 5, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 1, 3, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 5, 1, 4], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 5, 3, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 1, 5, 3, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 1, 5, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 1, 3, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 5, 1, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 1, 5, 3, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 806, 3670, 18051, 95163, 534587, 3184583, 20033482, 132598784, 920486604, 6683157656, 50624877667, 399216693973, 3270811078509, 27792444513157] "" "Class ", 1607, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 5, 3, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 1, 5, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 1, 3, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 5, 1, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 5, 3, 2], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 3, 1, 5, 2], [0, 1, 0, 0]]} "Class ", 1608, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 5, 3, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 1, 5, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 1, 3, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 5, 1, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 5, 3, 2], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 3, 1, 5, 2], [1, 1, 0, 0]]} "Class ", 1609, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 5, 3, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 1, 5, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 1, 3, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 5, 1, 4], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 5, 3, 2], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 3, 1, 5, 2], [0, 0, 1, 0]]} "Class ", 1610, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 5, 3, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 1, 5, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 1, 3, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 5, 1, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 5, 3, 2], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 3, 1, 5, 2], [1, 0, 1, 0]]} "Class ", 1611, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 5, 3, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 1, 5, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 1, 3, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 5, 1, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 5, 3, 2], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 3, 1, 5, 2], [0, 1, 1, 0]]} "Class ", 1612, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 5, 3, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 1, 5, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 1, 3, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 5, 1, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 5, 3, 2], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 3, 1, 5, 2], [1, 1, 1, 0]]} "Class ", 1613, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 5, 3, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 1, 5, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 1, 3, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 5, 1, 4], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 5, 3, 2], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 3, 1, 5, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 1, 5, 3, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 1, 5, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 1, 3, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 5, 1, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[4, 3, 1, 5, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 2, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 800, 3590, 17290, 88731, 482404, 2765093, 16642039, 104809426, 688647121, 4708331629, 33420907764, 245792788619, 1869529310843, 14682487562481] "" "Class ", 1614, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 5, 3, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 1, 5, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 1, 3, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 5, 1, 4], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 5, 3, 2], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 3, 1, 5, 2], [1, 0, 0, 1]]} "Class ", 1615, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 5, 3, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 1, 5, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 1, 3, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 5, 1, 4], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 5, 3, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 3, 1, 5, 2], [0, 1, 0, 1]]} "Class ", 1616, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 5, 3, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 1, 5, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 1, 3, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 5, 1, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 5, 3, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 3, 1, 5, 2], [1, 1, 0, 1]]} "Class ", 1617, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 5, 3, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 1, 5, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 1, 3, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 5, 1, 4], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 5, 3, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 3, 1, 5, 2], [0, 0, 1, 1]]} "Class ", 1618, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 5, 3, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 1, 5, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 1, 3, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 5, 1, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 5, 3, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 3, 1, 5, 2], [1, 0, 1, 1]]} "Class ", 1619, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 5, 3, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 1, 5, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 1, 3, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 5, 1, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 5, 3, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 3, 1, 5, 2], [0, 1, 1, 1]]} "Class ", 1620, " is:" {{[[1, 2, 3], [0, 1]], [[4, 1, 5, 3, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 1, 5, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 5, 1, 3, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 5, 1, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 1, 5, 3, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 3, 1, 5, 2], [1, 1, 1, 1]]} "Class ", 1621, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 1, 3, 5], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 5, 4, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 5, 3, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 3, 1, 2, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 1, 3, 5], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 3, 5, 4, 2], [0, 1, 0, 0]]} "Class ", 1622, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 1, 3, 5], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 5, 4, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 5, 3, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 3, 1, 2, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 1, 3, 5], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 3, 5, 4, 2], [1, 1, 0, 0]]} "Class ", 1623, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 1, 3, 5], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 5, 4, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 5, 3, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 3, 1, 2, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 1, 3, 5], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 3, 5, 4, 2], [0, 1, 1, 0]]} "Class ", 1624, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 1, 3, 5], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 5, 4, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 5, 3, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 3, 1, 2, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 1, 3, 5], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 3, 5, 4, 2], [1, 1, 1, 0]]} "Class ", 1625, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 1, 3, 5], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 5, 4, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 5, 3, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 3, 1, 2, 4], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 1, 3, 5], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 3, 5, 4, 2], [0, 1, 0, 1]]} "Class ", 1626, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 1, 3, 5], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 5, 4, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 5, 3, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 3, 1, 2, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 1, 3, 5], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 3, 5, 4, 2], [1, 1, 0, 1]]} "Class ", 1627, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 1, 3, 5], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 5, 4, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 5, 3, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 3, 1, 2, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 1, 3, 5], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 3, 5, 4, 2], [0, 1, 1, 1]]} "Class ", 1628, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 1, 3, 5], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 5, 4, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 5, 3, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 3, 1, 2, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 1, 3, 5], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 3, 5, 4, 2], [1, 1, 1, 1]]} "Class ", 1629, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 1, 5, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 5, 4, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 5, 1, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 1, 5, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 2, 1, 5, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 5, 4, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 5, 1, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 2, 1, 5, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[4, 3, 2, 5, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 830, 3834, 19150, 102562, 585492, 3544601, 22657284, 152350986, 1074183666, 7919108105, 60891394013, 487249507468, 4049460152431, 34890974398488] "" "Class ", 1630, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 1, 5, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 5, 4, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 5, 1, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 1, 2, 4], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 1, 5, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 2, 1, 5, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 5, 4, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 5, 1, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 1, 2, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 2, 1, 5, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 800, 3584, 17209, 87920, 475120, 2703248, 16127888, 100553246, 653242719, 4410576300, 30880302143, 223752362416, 1674858997074, 12930600036868] "" "Class ", 1631, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 1, 5, 3], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 5, 4, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 5, 1, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 1, 2, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 1, 5, 3], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 1, 5, 4, 2], [0, 1, 0, 0]]} "Class ", 1632, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 1, 5, 3], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 5, 4, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 5, 1, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 1, 2, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 1, 5, 3], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 1, 5, 4, 2], [1, 1, 0, 0]]} "Class ", 1633, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 1, 5, 3], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 5, 4, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 5, 1, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 1, 2, 4], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 1, 5, 3], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 1, 5, 4, 2], [0, 0, 1, 0]]} "Class ", 1634, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 1, 5, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 5, 4, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 5, 1, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 1, 2, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 1, 5, 3], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[3, 1, 5, 4, 2], [1, 0, 1, 0]]} "Class ", 1635, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 1, 5, 3], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 5, 4, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 5, 1, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 1, 2, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 1, 5, 3], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 1, 5, 4, 2], [0, 1, 1, 0]]} "Class ", 1636, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 1, 5, 3], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 5, 4, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 5, 1, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 1, 2, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 1, 5, 3], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 1, 5, 4, 2], [1, 1, 1, 0]]} "Class ", 1637, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 1, 5, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 5, 4, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 5, 1, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 1, 5, 3], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 1, 5, 4, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 2, 1, 5, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 5, 4, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 5, 1, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[3, 1, 5, 4, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 3}, {[0, 1, 0, 0, 0]}], [[3, 1, 4, 2], {1, 3}, {}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 808, 3644, 17641, 90982, 497031, 2862327, 17305620, 109469092, 722333371, 4959028561, 35340844611, 260914991956, 1991945914147, 15700257773736] "" "Class ", 1638, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 1, 5, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 5, 4, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 5, 1, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 1, 2, 4], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 1, 5, 3], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[3, 1, 5, 4, 2], [1, 0, 0, 1]]} "Class ", 1639, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 1, 5, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 5, 4, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 5, 1, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 1, 2, 4], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 1, 5, 3], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 1, 5, 4, 2], [0, 1, 0, 1]]} "Class ", 1640, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 1, 5, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 5, 4, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 5, 1, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 1, 2, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 1, 5, 3], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 1, 5, 4, 2], [1, 1, 0, 1]]} "Class ", 1641, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 1, 5, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 5, 4, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 5, 1, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 1, 2, 4], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 1, 5, 3], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 1, 5, 4, 2], [0, 0, 1, 1]]} "Class ", 1642, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 1, 5, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 5, 4, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 5, 1, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 1, 2, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 1, 5, 3], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[3, 1, 5, 4, 2], [1, 0, 1, 1]]} "Class ", 1643, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 1, 5, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 5, 4, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 5, 1, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 1, 2, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 1, 5, 3], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 1, 5, 4, 2], [0, 1, 1, 1]]} "Class ", 1644, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 1, 5, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 5, 4, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 5, 1, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 5, 1, 2, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 1, 5, 3], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 1, 5, 4, 2], [1, 1, 1, 1]]} "Class ", 1645, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 3, 1, 5], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 3, 4, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 3, 5, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 3, 2, 4], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 3, 1, 5], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[1, 5, 3, 4, 2], [0, 0, 1, 0]]} "Class ", 1646, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 3, 1, 5], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 3, 4, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 3, 5, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 3, 2, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 3, 1, 5], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[1, 5, 3, 4, 2], [1, 0, 1, 0]]} "Class ", 1647, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 3, 1, 5], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 3, 4, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 3, 5, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 3, 2, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 3, 1, 5], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 5, 3, 4, 2], [0, 1, 1, 0]]} "Class ", 1648, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 3, 1, 5], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 3, 4, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 3, 5, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 3, 2, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 3, 1, 5], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 5, 3, 4, 2], [1, 1, 1, 0]]} "Class ", 1649, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 3, 1, 5], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 3, 4, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 3, 5, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 3, 2, 4], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 3, 1, 5], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[1, 5, 3, 4, 2], [0, 0, 1, 1]]} "Class ", 1650, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 3, 1, 5], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 3, 4, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 3, 5, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 3, 2, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 3, 1, 5], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[1, 5, 3, 4, 2], [1, 0, 1, 1]]} "Class ", 1651, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 3, 1, 5], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 3, 4, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 3, 5, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 3, 2, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 3, 1, 5], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 5, 3, 4, 2], [0, 1, 1, 1]]} "Class ", 1652, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 3, 1, 5], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 3, 4, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 3, 5, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 3, 2, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 3, 1, 5], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 5, 3, 4, 2], [1, 1, 1, 1]]} "Class ", 1653, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 3, 5, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 3, 4, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 3, 1, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 3, 2, 4], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 3, 5, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 1, 3, 4, 2], [0, 0, 1, 0]]} "Class ", 1654, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 3, 5, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 3, 4, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 3, 1, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 3, 2, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 3, 5, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 1, 3, 4, 2], [1, 0, 1, 0]]} "Class ", 1655, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 3, 5, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 3, 4, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 3, 1, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 3, 2, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 3, 5, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 1, 3, 4, 2], [0, 1, 1, 0]]} "Class ", 1656, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 3, 5, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 3, 4, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 3, 1, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 3, 2, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 3, 5, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 1, 3, 4, 2], [1, 1, 1, 0]]} "Class ", 1657, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 3, 5, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 3, 4, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 3, 1, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 3, 2, 4], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 3, 5, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 1, 3, 4, 2], [0, 0, 1, 1]]} "Class ", 1658, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 3, 5, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 3, 4, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 3, 1, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 3, 2, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 3, 5, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 1, 3, 4, 2], [1, 0, 1, 1]]} "Class ", 1659, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 3, 5, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 3, 4, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 3, 1, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 3, 2, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 3, 5, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 1, 3, 4, 2], [0, 1, 1, 1]]} "Class ", 1660, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 3, 5, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 3, 4, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 3, 1, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 3, 2, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 3, 5, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 1, 3, 4, 2], [1, 1, 1, 1]]} "Class ", 1661, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 1, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 1, 4, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 5, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 5, 2, 4], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 5, 1, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 1, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 1, 4, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 5, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 5, 2, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 2, 5, 1, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [ [3, 2, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}] , [[4, 2, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [ [4, 3, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 198, 850, 3991, 20295, 110902, 646824, 4005415, 26215393, 180646378, 1306205116, 9881724641, 78013981469, 641260307188, 5476803337918, 48511899988525] "" "Class ", 1662, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 1, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 1, 4, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 5, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 5, 2, 4], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 5, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 1, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 1, 4, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 5, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 5, 2, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 2, 5, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 831, 3843, 19205, 102993, 588979, 3573374, 22902192, 154486316, 1093230643, 8093018048, 62516809530, 502804344444, 4201888068327, 36420450427715] "" "Class ", 1663, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 1, 3], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 1, 4, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 5, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 5, 2, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 5, 1, 3], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 5, 1, 4, 2], [0, 1, 0, 0]]} "Class ", 1664, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 1, 3], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 1, 4, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 5, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 5, 2, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 5, 1, 3], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 5, 1, 4, 2], [1, 1, 0, 0]]} "Class ", 1665, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 1, 3], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 1, 4, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 5, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 5, 2, 4], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 5, 1, 3], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 5, 1, 4, 2], [0, 0, 1, 0]]} "Class ", 1666, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 1, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 1, 4, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 5, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 5, 2, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 5, 1, 3], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[3, 5, 1, 4, 2], [1, 0, 1, 0]]} "Class ", 1667, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 1, 3], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 1, 4, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 5, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 5, 2, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 5, 1, 3], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 5, 1, 4, 2], [0, 1, 1, 0]]} "Class ", 1668, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 1, 3], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 1, 4, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 5, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 5, 2, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 5, 1, 3], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 5, 1, 4, 2], [1, 1, 1, 0]]} "Class ", 1669, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 1, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 1, 4, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 5, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 5, 2, 4], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 5, 1, 3], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 5, 1, 4, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 1, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 1, 4, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 5, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 5, 2, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[3, 5, 1, 4, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 833, 3864, 19395, 104549, 601381, 3672209, 23699913, 161048976, 1148492946, 8570439412, 66753221923, 541435215701, 4563928265057, 39907001120231] "" "Class ", 1670, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 1, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 1, 4, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 5, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 5, 2, 4], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 5, 1, 3], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[3, 5, 1, 4, 2], [1, 0, 0, 1]]} "Class ", 1671, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 1, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 1, 4, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 5, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 5, 2, 4], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 5, 1, 3], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 5, 1, 4, 2], [0, 1, 0, 1]]} "Class ", 1672, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 1, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 1, 4, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 5, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 5, 2, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 5, 1, 3], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 5, 1, 4, 2], [1, 1, 0, 1]]} "Class ", 1673, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 1, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 1, 4, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 5, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 5, 2, 4], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 5, 1, 3], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 5, 1, 4, 2], [0, 0, 1, 1]]} "Class ", 1674, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 1, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 1, 4, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 5, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 5, 2, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 5, 1, 3], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[3, 5, 1, 4, 2], [1, 0, 1, 1]]} "Class ", 1675, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 1, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 1, 4, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 5, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 5, 2, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 5, 1, 3], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 5, 1, 4, 2], [0, 1, 1, 1]]} "Class ", 1676, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 1, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 1, 4, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 5, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 5, 2, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 5, 1, 3], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 5, 1, 4, 2], [1, 1, 1, 1]]} "Class ", 1677, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 3, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 1, 4, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 3, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 5, 2, 4], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 5, 3, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 3, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 1, 4, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 3, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 5, 2, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 2, 5, 3, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [ [3, 1, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}] , [[4, 1, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 1, 5, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[4, 2, 5, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 837, 3904, 19696, 106647, 616210, 3779110, 24488209, 167023273, 1195171218, 8946834710, 69885382074, 568322986437, 4801918139922, 42077603472674] "" "Class ", 1678, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 3, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 1, 4, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 3, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 5, 2, 4], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 5, 3, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 3, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 1, 4, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 3, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 5, 2, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 2, 5, 3, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 806, 3670, 18051, 95163, 534587, 3184583, 20033482, 132598784, 920486604, 6683157656, 50624877667, 399216693973, 3270811078509, 27792444513157] "" "Class ", 1679, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 3, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 1, 4, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 3, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 5, 2, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 5, 3, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 3, 1, 4, 2], [0, 1, 0, 0]]} "Class ", 1680, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 3, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 1, 4, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 3, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 5, 2, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 5, 3, 1], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 3, 1, 4, 2], [1, 1, 0, 0]]} "Class ", 1681, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 3, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 1, 4, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 3, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 5, 2, 4], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 5, 3, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 3, 1, 4, 2], [0, 0, 1, 0]]} "Class ", 1682, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 3, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 1, 4, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 3, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 5, 2, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 5, 3, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 3, 1, 4, 2], [1, 0, 1, 0]]} "Class ", 1683, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 3, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 1, 4, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 3, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 5, 2, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 5, 3, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 3, 1, 4, 2], [0, 1, 1, 0]]} "Class ", 1684, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 3, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 1, 4, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 3, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 5, 2, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 5, 3, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 3, 1, 4, 2], [1, 1, 1, 0]]} "Class ", 1685, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 3, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 1, 4, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 3, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 5, 2, 4], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 5, 3, 1], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 3, 1, 4, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 3, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 1, 4, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 3, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 5, 2, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 3, 1, 4, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 815, 3732, 18443, 97625, 550370, 3288509, 20737426, 137511671, 955865461, 6946143073, 52641758235, 415161323552, 3400630000892, 28879973055369] "" "Class ", 1686, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 3, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 1, 4, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 3, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 5, 2, 4], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 5, 3, 1], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 3, 1, 4, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 3, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 1, 4, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 3, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 5, 2, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 3, 1, 4, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {3}, {}], [[4, 2, 1, 3], {2}, {[0, 1, 0, 0, 0]}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 778, 3408, 15924, 78844, 411475, 2253697, 12908069, 77075619, 478546545, 3082415602, 20556346424, 141682060856, 1007643116969, 7384133650021] "" "Class ", 1687, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 3, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 1, 4, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 3, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 5, 2, 4], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 5, 3, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 3, 1, 4, 2], [0, 1, 0, 1]]} "Class ", 1688, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 3, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 1, 4, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 3, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 5, 2, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 5, 3, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 3, 1, 4, 2], [1, 1, 0, 1]]} "Class ", 1689, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 3, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 1, 4, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 3, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 5, 2, 4], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 5, 3, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 3, 1, 4, 2], [0, 0, 1, 1]]} "Class ", 1690, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 3, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 1, 4, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 3, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 5, 2, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 5, 3, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 3, 1, 4, 2], [1, 0, 1, 1]]} "Class ", 1691, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 3, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 1, 4, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 3, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 5, 2, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 5, 3, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 3, 1, 4, 2], [0, 1, 1, 1]]} "Class ", 1692, " is:" {{[[1, 2, 3], [0, 1]], [[4, 2, 5, 3, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 1, 4, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 4, 1, 3, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 5, 2, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 2, 5, 3, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 3, 1, 4, 2], [1, 1, 1, 1]]} "Class ", 1693, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 1, 2, 5], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 5, 3, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 5, 4, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 1, 3, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 1, 2, 5], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 4, 5, 3, 2], [0, 1, 0, 0]]} "Class ", 1694, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 1, 2, 5], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 5, 3, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 5, 4, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 1, 3, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 1, 2, 5], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 4, 5, 3, 2], [1, 1, 0, 0]]} "Class ", 1695, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 1, 2, 5], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 5, 3, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 5, 4, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 1, 3, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 1, 2, 5], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 4, 5, 3, 2], [0, 1, 1, 0]]} "Class ", 1696, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 1, 2, 5], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 5, 3, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 5, 4, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 1, 3, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 1, 2, 5], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 4, 5, 3, 2], [1, 1, 1, 0]]} "Class ", 1697, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 1, 2, 5], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 5, 3, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 5, 4, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 1, 3, 4], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 1, 2, 5], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 4, 5, 3, 2], [0, 1, 0, 1]]} "Class ", 1698, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 1, 2, 5], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 5, 3, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 5, 4, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 1, 3, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 1, 2, 5], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 4, 5, 3, 2], [1, 1, 0, 1]]} "Class ", 1699, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 1, 2, 5], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 5, 3, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 5, 4, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 1, 3, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 1, 2, 5], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 4, 5, 3, 2], [0, 1, 1, 1]]} "Class ", 1700, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 1, 2, 5], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 4, 5, 3, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 5, 4, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 2, 1, 3, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 1, 2, 5], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 4, 5, 3, 2], [1, 1, 1, 1]]} "Class ", 1701, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 1, 5, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 5, 3, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 5, 1, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 1, 3, 4], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 1, 5, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 3, 1, 5, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 5, 3, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 5, 1, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 1, 3, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 3, 1, 5, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[4, 2, 1, 5, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 833, 3865, 19400, 104485, 600187, 3658102, 23552343, 159583709, 1134221682, 8431805899, 65397329083, 528006096415, 4428756678852, 38521166042497] "" "Class ", 1702, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 1, 5, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 5, 3, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 5, 1, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 1, 3, 4], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 1, 5, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 3, 1, 5, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 5, 3, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 5, 1, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 1, 3, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 3, 1, 5, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 800, 3584, 17209, 87920, 475120, 2703248, 16127888, 100553246, 653242719, 4410576300, 30880302143, 223752362416, 1674858997074, 12930600036868] "" "Class ", 1703, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 1, 5, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 5, 3, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 5, 1, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 1, 3, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 1, 5, 2], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 1, 5, 3, 2], [0, 1, 0, 0]]} "Class ", 1704, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 1, 5, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 5, 3, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 5, 1, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 1, 3, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 1, 5, 2], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 1, 5, 3, 2], [1, 1, 0, 0]]} "Class ", 1705, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 1, 5, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 5, 3, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 5, 1, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 1, 3, 4], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 1, 5, 2], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 1, 5, 3, 2], [0, 0, 1, 0]]} "Class ", 1706, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 1, 5, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 5, 3, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 5, 1, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 1, 3, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 1, 5, 2], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 1, 5, 3, 2], [1, 0, 1, 0]]} "Class ", 1707, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 1, 5, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 5, 3, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 5, 1, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 1, 3, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 1, 5, 2], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 1, 5, 3, 2], [0, 1, 1, 0]]} "Class ", 1708, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 1, 5, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 5, 3, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 5, 1, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 1, 3, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 1, 5, 2], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 1, 5, 3, 2], [1, 1, 1, 0]]} "Class ", 1709, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 1, 5, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 5, 3, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 5, 1, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 1, 3, 4], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 1, 5, 2], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 1, 5, 3, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 3, 1, 5, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 5, 3, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 5, 1, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 1, 3, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[4, 1, 5, 3, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 3}, {}], [[3, 1, 4, 2], {1, 3}, {[0, 1, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 821, 3768, 18657, 98960, 558971, 3345821, 21133641, 140358785, 977114962, 7110637203, 53960903935, 426109407173, 3494565359914, 29712276754586] "" "Class ", 1710, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 1, 5, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 5, 3, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 5, 1, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 1, 3, 4], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 1, 5, 2], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 1, 5, 3, 2], [1, 0, 0, 1]]} "Class ", 1711, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 1, 5, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 5, 3, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 5, 1, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 1, 3, 4], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 1, 5, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 1, 5, 3, 2], [0, 1, 0, 1]]} "Class ", 1712, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 1, 5, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 5, 3, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 5, 1, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 1, 3, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 1, 5, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 1, 5, 3, 2], [1, 1, 0, 1]]} "Class ", 1713, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 1, 5, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 5, 3, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 5, 1, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 1, 3, 4], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 1, 5, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 1, 5, 3, 2], [0, 0, 1, 1]]} "Class ", 1714, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 1, 5, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 5, 3, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 5, 1, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 1, 3, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 1, 5, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 1, 5, 3, 2], [1, 0, 1, 1]]} "Class ", 1715, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 1, 5, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 5, 3, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 5, 1, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 1, 3, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 1, 5, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 1, 5, 3, 2], [0, 1, 1, 1]]} "Class ", 1716, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 1, 5, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 1, 5, 3, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 5, 1, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 5, 1, 3, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 1, 5, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 1, 5, 3, 2], [1, 1, 1, 1]]} "Class ", 1717, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {}, {}], [[4, 3, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [ [5, 3, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}] , [[5, 4, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [5, 4, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 827, 3795, 18755, 99146, 556711, 3305017, 20655285, 135399720, 927973061, 6631556521, 49294051497, 380306658250, 3039453750685, 25120541332271] "" "Class ", 1718, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 827, 3795, 18755, 99146, 556711, 3305017, 20655285, 135399720, 927973061, 6631556521, 49294051497, 380306658250, 3039453750685, 25120541332271] "" "Class ", 1719, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 4, 3, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 5, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 2, 3, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 5, 4, 3, 2], [0, 1, 0, 0]]} "Class ", 1720, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 4, 3, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 5, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 5, 4, 3, 2], [1, 1, 0, 0]]} "Class ", 1721, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 1, 5], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 4, 3, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 5, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 2, 3, 4], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 2, 1, 5], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[1, 5, 4, 3, 2], [0, 0, 1, 0]]} "Class ", 1722, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 1, 5], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 4, 3, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 5, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 2, 3, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 2, 1, 5], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[1, 5, 4, 3, 2], [1, 0, 1, 0]]} "Class ", 1723, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 1, 5], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 4, 3, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 5, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 2, 3, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 2, 1, 5], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 5, 4, 3, 2], [0, 1, 1, 0]]} "Class ", 1724, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 1, 5], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 4, 3, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 5, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 2, 3, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 2, 1, 5], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 5, 4, 3, 2], [1, 1, 1, 0]]} "Class ", 1725, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 1, 5], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 5, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 2, 1, 5], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 1, 5], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 5, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 815, 3686, 17882, 92261, 503285, 2888967, 17374721, 109101403, 713172291, 4840150119, 34027903651, 247316785101, 1854946810551, 14334190857590] "" "Class ", 1726, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 1, 5], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 5, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 2, 1, 5], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 1, 5], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 5, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 815, 3686, 17882, 92261, 503285, 2888967, 17374721, 109101403, 713172291, 4840150119, 34027903651, 247316785101, 1854946810551, 14334190857590] "" "Class ", 1727, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 1, 5], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 4, 3, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 5, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 2, 3, 4], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 2, 1, 5], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 5, 4, 3, 2], [0, 1, 0, 1]]} "Class ", 1728, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 1, 5], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 5, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 2, 1, 5], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]} "Class ", 1729, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 1, 5], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 4, 3, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 5, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 2, 3, 4], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 2, 1, 5], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[1, 5, 4, 3, 2], [0, 0, 1, 1]]} "Class ", 1730, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 1, 5], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 4, 3, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 5, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 2, 3, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 2, 1, 5], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[1, 5, 4, 3, 2], [1, 0, 1, 1]]} "Class ", 1731, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 1, 5], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 4, 3, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 5, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 2, 3, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 2, 1, 5], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 5, 4, 3, 2], [0, 1, 1, 1]]} "Class ", 1732, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 5, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]} "Class ", 1733, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 4, 3, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 1, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 2, 3, 4], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 4, 3, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 1, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 2, 3, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[4, 2, 1, 5, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[4, 3, 1, 5, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[4, 3, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 837, 3900, 19660, 106401, 614461, 3766285, 24391241, 166273511, 1189199516, 8897662825, 69467109081, 564650817794, 4768666898714, 41767236529799] "" "Class ", 1734, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 4, 3, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 1, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 2, 3, 4], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 4, 3, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 1, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 2, 3, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 800, 3584, 17209, 87920, 475120, 2703248, 16127888, 100553246, 653242719, 4410576300, 30880302143, 223752362416, 1674858997074, 12930600036868] "" "Class ", 1735, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 4, 3, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 1, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 2, 3, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 1, 4, 3, 2], [0, 1, 0, 0]]} "Class ", 1736, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 4, 3, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 1, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 2, 3, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 1, 4, 3, 2], [1, 1, 0, 0]]} "Class ", 1737, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 4, 3, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 1, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 2, 3, 4], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 1, 4, 3, 2], [0, 0, 1, 0]]} "Class ", 1738, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 4, 3, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 1, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 2, 3, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 1, 4, 3, 2], [1, 0, 1, 0]]} "Class ", 1739, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 4, 3, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 1, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 2, 3, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 1, 4, 3, 2], [0, 1, 1, 0]]} "Class ", 1740, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 4, 3, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 1, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 2, 3, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 1, 4, 3, 2], [1, 1, 1, 0]]} "Class ", 1741, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 4, 3, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 1, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 2, 3, 4], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 1, 4, 3, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 4, 3, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 1, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 2, 3, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 1, 4, 3, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 3}, {[0, 1, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 825, 3804, 18945, 101196, 576319, 3481258, 22208738, 149090234, 1049861928, 7733112934, 59434503030, 475582557883, 3954159212576, 34099160564016] "" "Class ", 1742, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 4, 3, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 1, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 2, 3, 4], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 1, 4, 3, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 4, 3, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 1, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 2, 3, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 1, 4, 3, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 785, 3442, 16034, 78788, 406132, 2186424, 12248931, 71196625, 428278940, 2660538590, 17036716025, 112273466170, 760377593318, 5285649353082] "" "Class ", 1743, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 4, 3, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 1, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 2, 3, 4], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 1, 4, 3, 2], [0, 1, 0, 1]]} "Class ", 1744, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 4, 3, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 1, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 2, 3, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 1, 4, 3, 2], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 4, 3, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 1, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 2, 3, 4], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 1, 4, 3, 2], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {}, {}], [[3, 2, 4, 1], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {4}, {}], [[3, 1, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 5, 4, 2], {4}, {}], [[3, 2, 5, 4, 1], {1, 2, 4}, {}], [[4, 1, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 5, 3, 2], {1, 4}, {[0, 1, 0, 0, 0, 0]}], [[4, 2, 5, 3, 1], {1, 2, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 773, 3336, 15207, 72697, 362447, 1876392, 10051083, 55544661, 315899245, 1845139684, 11048651523, 67719859612, 424287619507, 2714074517843] "" "Class ", 1745, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 4, 3, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 1, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 2, 3, 4], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 1, 4, 3, 2], [0, 0, 1, 1]]} "Class ", 1746, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 4, 3, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 1, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 2, 3, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 1, 4, 3, 2], [1, 0, 1, 1]]} "Class ", 1747, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 4, 3, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 1, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 2, 3, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 1, 4, 3, 2], [0, 1, 1, 1]]} "Class ", 1748, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 1, 4, 3, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 4, 1, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 5, 2, 3, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 2, 5, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 1, 4, 3, 2], [1, 1, 1, 1]]} "Class ", 1749, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 1, 3, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 5, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 5, 3, 4], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 1, 3, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 5, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 5, 3, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [ [3, 2, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}] , [[4, 2, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 3, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 199, 858, 4043, 20626, 113025, 660870, 4101540, 26898055, 185682476, 1344791270, 10188544670, 80543512108, 662859095395, 5667595180615, 50253461507758] "" "Class ", 1750, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 1, 3, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 5, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 5, 3, 4], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 1, 3, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 5, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 5, 3, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 831, 3843, 19205, 102993, 588979, 3573374, 22902192, 154486316, 1093230643, 8093018048, 62516809530, 502804344444, 4201888068327, 36420450427715] "" "Class ", 1751, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 5, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 0]]} "Class ", 1752, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 1, 3, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 5, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 5, 3, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 5, 1, 3, 2], [1, 1, 0, 0]]} "Class ", 1753, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 1, 3, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 5, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 5, 3, 4], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 5, 1, 3, 2], [0, 0, 1, 0]]} "Class ", 1754, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 1, 3, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 5, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 5, 3, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 5, 1, 3, 2], [1, 0, 1, 0]]} "Class ", 1755, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 1, 3, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 5, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 5, 3, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 5, 1, 3, 2], [0, 1, 1, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 1, 3, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 5, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 5, 3, 4], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[4, 5, 1, 3, 2], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {4}, {}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {4}, {}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {4}, {}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {4}, {}], [[3, 5, 2, 4, 1], {2, 3}, {}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 799, 3581, 17225, 88353, 480705, 2762125, 16699561, 105896837, 702375905, 4860713661, 35020702065, 262175127733, 2035771570009, 16369545462221] "" "Class ", 1756, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 1, 3, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 5, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 5, 3, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 5, 1, 3, 2], [1, 1, 1, 0]]} "Class ", 1757, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 5, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 5, 3, 4], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 5, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 5, 3, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 198, 849, 3981, 20220, 110340, 642717, 3974980, 25984555, 178846428, 1291743613, 9761855424, 76988703614, 632212817175, 5394471913534, 47739780774299] "" "Class ", 1758, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 1, 3, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 5, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 5, 3, 4], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 5, 1, 3, 2], [1, 0, 0, 1]]} "Class ", 1759, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 5, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]} "Class ", 1760, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 1, 3, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 5, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 5, 3, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 5, 1, 3, 2], [1, 1, 0, 1]]} "Class ", 1761, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 1, 3, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 5, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 5, 3, 4], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 5, 1, 3, 2], [0, 0, 1, 1]]} "Class ", 1762, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 1, 3, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 5, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 5, 3, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 5, 1, 3, 2], [1, 0, 1, 1]]} "Class ", 1763, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 1, 3, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 5, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 5, 3, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 5, 1, 3, 2], [0, 1, 1, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 1, 3, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 5, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 5, 3, 4], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[4, 5, 1, 3, 2], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {4}, {}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {4}, {}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {4}, {[0, 1, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {4}, {[0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {2, 3}, {}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3, 4}, {[0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 787, 3474, 16385, 82086, 434787, 2425495, 14204293, 87075908, 557370385, 3716917695, 25771442227, 185446213578, 1382608160683, 10664068755489] "" "Class ", 1764, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 1, 3, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 5, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 5, 3, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 5, 1, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 5, 1, 3, 2], [1, 1, 1, 1]]} "Class ", 1765, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 1, 3, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 4, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 5, 3, 4], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 1, 3, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 4, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 5, 3, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [ [3, 2, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}] , [[4, 2, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 3, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 837, 3903, 19685, 106566, 615616, 3774631, 24453374, 166747377, 1192930152, 8928073983, 69723447161, 566882772509, 4788727140484, 41953220810459] "" "Class ", 1766, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 5, 3, 4], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 5, 3, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 812, 3729, 18513, 98622, 560625, 3382881, 21571376, 144816179, 1020235123, 7521133741, 57871063268, 463715758085, 3861657143379, 33360429966454] "" "Class ", 1767, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 2, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 4, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 5, 3, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 5, 2, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 0]]} "Class ", 1768, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 2, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 1, 3, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 4, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 5, 3, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 5, 2, 1], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 4, 1, 3, 2], [1, 1, 0, 0]]} "Class ", 1769, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 2, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 1, 3, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 4, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 5, 3, 4], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 5, 2, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 4, 1, 3, 2], [0, 0, 1, 0]]} "Class ", 1770, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 2, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 1, 3, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 4, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 5, 3, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 5, 2, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 4, 1, 3, 2], [1, 0, 1, 0]]} "Class ", 1771, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 2, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 1, 3, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 4, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 5, 3, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 5, 2, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 4, 1, 3, 2], [0, 1, 1, 0]]} "Class ", 1772, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 2, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 1, 3, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 4, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 5, 3, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 5, 2, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 4, 1, 3, 2], [1, 1, 1, 0]]} "Class ", 1773, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 2, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 4, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 5, 3, 4], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 5, 2, 1], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 2, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 4, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 5, 3, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 825, 3804, 18945, 101196, 576319, 3481258, 22208738, 149090234, 1049861928, 7733112934, 59434503030, 475582557883, 3954159212576, 34099160564016] "" "Class ", 1774, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 2, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 4, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 5, 3, 4], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 5, 2, 1], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 2, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 4, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 5, 3, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {3}, {}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 799, 3614, 17599, 91756, 509518, 2998629, 18629532, 121776791, 835064573, 5991141262, 44864808867, 349934846763, 2837369228685, 23874137907775] "" "Class ", 1775, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 2, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 4, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 5, 3, 4], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 5, 2, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]} "Class ", 1776, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 2, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 4, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 5, 3, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 5, 2, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]} "Class ", 1777, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 2, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 1, 3, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 4, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 5, 3, 4], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 5, 2, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 4, 1, 3, 2], [0, 0, 1, 1]]} "Class ", 1778, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 2, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 1, 3, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 4, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 5, 3, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 5, 2, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 4, 1, 3, 2], [1, 0, 1, 1]]} "Class ", 1779, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 2, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 4, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 5, 3, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 5, 2, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]} "Class ", 1780, " is:" {{[[1, 2, 3], [0, 1]], [[4, 3, 5, 2, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 1, 3, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 3, 1, 4, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 5, 3, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 3, 5, 2, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 4, 1, 3, 2], [1, 1, 1, 1]]} "Class ", 1781, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 1, 2, 3], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 5, 1, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 5, 4, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 1, 5, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 1, 2, 3], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 4, 5, 1, 2], [0, 1, 0, 0]]} "Class ", 1782, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 1, 2, 3], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 5, 1, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 5, 4, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 1, 5, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 1, 2, 3], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 4, 5, 1, 2], [1, 1, 0, 0]]} "Class ", 1783, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 5, 1, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 1, 5, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 4, 5, 1, 2], [0, 1, 1, 0]]} "Class ", 1784, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 5, 1, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 1, 5, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 4, 5, 1, 2], [1, 1, 1, 0]]} "Class ", 1785, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 1, 2, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 5, 1, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 5, 4, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 1, 5, 4], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 1, 2, 3], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 4, 5, 1, 2], [0, 1, 0, 1]]} "Class ", 1786, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 1, 2, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 5, 1, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 5, 4, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 1, 5, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 1, 2, 3], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 4, 5, 1, 2], [1, 1, 0, 1]]} "Class ", 1787, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 5, 1, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 1, 5, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 4, 5, 1, 2], [0, 1, 1, 1]]} "Class ", 1788, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 5, 1, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 1, 5, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 4, 5, 1, 2], [1, 1, 1, 1]]} "Class ", 1789, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 5, 3, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 5, 4], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 5, 3, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 5, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 198, 851, 4000, 20365, 111383, 650217, 4029788, 26395057, 182012372, 1316939159, 9968926213, 78746312437, 647615186284, 5533744268483, 49038295523636] "" "Class ", 1790, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 5, 3, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 5, 4], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 5, 3, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 5, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 197, 845, 3965, 20157, 110111, 642147, 3976399, 26026469, 179358437, 1297030613, 9813540115, 77486255121, 637014108971, 5441342362847, 48205003289963] "" "Class ", 1791, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 5, 3, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 5, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [0, 1, 0, 0]]} "Class ", 1792, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 5, 3, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 5, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [1, 1, 0, 0]]} "Class ", 1793, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 5, 4], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 5, 4], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 813, 3710, 18271, 96438, 542411, 3234981, 20373067, 134993858, 938159857, 6819295487, 51716780923, 408315663404, 3349445730949, 28496029499393] "" "Class ", 1794, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 805, 3659, 17951, 94389, 528945, 3143623, 19730731, 130308305, 902709725, 6541297827, 49459063191, 389344871821, 3184690517545, 27018703063391] "" "Class ", 1795, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 5, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [0, 1, 1, 0]]} "Class ", 1796, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 5, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [1, 1, 1, 0]]} "Class ", 1797, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 5, 3, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 5, 4], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 5, 3, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 5, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 3}, {}], [[3, 1, 4, 2], {1, 3}, {}], [[3, 2, 4, 1], {1, 2}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 814, 3724, 18410, 97647, 552404, 3316442, 21040063, 140532532, 985059987, 7225569594, 55323722328, 441167478294, 3656538316673, 31442533947795] "" "Class ", 1798, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 5, 3, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 5, 4], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 5, 3, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 5, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {2}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 3}, {}], [[3, 1, 4, 2], {1, 3}, {}], [[3, 2, 4, 1], {1, 3}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 803, 3637, 17783, 93232, 521179, 3091599, 19379685, 127910610, 886105779, 6424885499, 48636309535, 383529424213, 3144151720535, 26747408118351] "" "Class ", 1799, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 5, 3, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 5, 4], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [0, 1, 0, 1]]} "Class ", 1800, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 5, 3, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 5, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [1, 1, 0, 1]]} "Class ", 1801, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 5, 4], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 5, 4], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {}], [[3, 1, 4, 2], {}, {}], [[3, 2, 4, 1], {}, {[0, 1, 0, 0, 0]}], [[3, 1, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 4, 1, 5], {1, 2}, {[0, 1, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 3}, {[0, 1, 0, 0, 0, 0]}], [[4, 1, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 5, 3, 2], {4}, {}], [[4, 2, 5, 1, 3], {1, 3}, {[0, 1, 0, 0, 0, 0]}], [[4, 2, 5, 3, 1], {4}, {[0, 1, 0, 0, 0, 0]}], [[4, 3, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 775, 3372, 15623, 76686, 397185, 2163378, 12355687, 73802848, 459985275, 2985173353, 20133717601, 140881530909, 1021105607513, 7654925923951] "" "Class ", 1802, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {2}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {}], [[3, 1, 4, 2], {}, {}], [[3, 2, 4, 1], {}, {[0, 1, 0, 0, 0]}], [[3, 1, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 4, 1, 5], {1, 2}, {[0, 1, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 3}, {[0, 1, 0, 0, 0, 0]}], [[4, 1, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 5, 3, 2], {4}, {}], [[4, 2, 5, 1, 3], {1, 3}, {[0, 1, 0, 0, 0, 0]}], [[4, 2, 5, 3, 1], {4}, {[0, 1, 0, 0, 0, 0]}], [[4, 3, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 763, 3275, 14945, 72210, 368121, 1973863, 11100775, 65312294, 401090351, 2565591651, 17060988933, 117743457754, 841962671965, 6229249601951] "" "Class ", 1803, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 5, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [0, 1, 1, 1]]} "Class ", 1804, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 5, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 3, 5, 1, 2], [1, 1, 1, 1]]} "Class ", 1805, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 1, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 5, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 5, 4], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 1, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 5, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 5, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 5, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 198, 850, 3992, 20300, 110932, 647014, 4006662, 26223796, 180705775, 1306642754, 9885082514, 78040780848, 641482500479, 5478714100296, 48528919085173] "" "Class ", 1806, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 1, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 5, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 5, 4], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 1, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 5, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 5, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 831, 3843, 19205, 102993, 588979, 3573374, 22902192, 154486316, 1093230643, 8093018048, 62516809530, 502804344444, 4201888068327, 36420450427715] "" "Class ", 1807, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 1, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 5, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 5, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 5, 4, 1, 2], [0, 1, 0, 0]]} "Class ", 1808, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 1, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 5, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 5, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 5, 4, 1, 2], [1, 1, 0, 0]]} "Class ", 1809, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 1, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 5, 4], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 1, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 5, 4], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 821, 3767, 18651, 98985, 559717, 3355743, 21241839, 141455297, 987871045, 7214952159, 54973114379, 436010754885, 3592659920317, 30699513115991] "" "Class ", 1810, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 1, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 5, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 1, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 5, 4], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 806, 3623, 17452, 89537, 486489, 2787306, 16776323, 105740391, 696000655, 4772555499, 34019507603, 251597026924, 1927216912646, 15265889573205] "" "Class ", 1811, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 1, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 5, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 5, 4, 1, 2], [0, 1, 1, 0]]} "Class ", 1812, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 1, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 5, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 5, 4, 1, 2], [1, 1, 1, 0]]} "Class ", 1813, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 1, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 5, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 5, 4], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 5, 4, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 1, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 5, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 5, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[3, 5, 4, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 813, 3711, 18284, 96537, 543033, 3238472, 20390302, 135055424, 938085081, 6814213059, 51638007015, 407336849070, 3338214816532, 28371277612346] "" "Class ", 1814, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 1, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 5, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 5, 4], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[3, 5, 4, 1, 2], [1, 0, 0, 1]]} "Class ", 1815, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 1, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 5, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 5, 4], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 5, 4, 1, 2], [0, 1, 0, 1]]} "Class ", 1816, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 1, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 5, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 5, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 5, 4, 1, 2], [1, 1, 0, 1]]} "Class ", 1817, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 1, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 5, 4], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 5, 4, 1, 2], [0, 0, 1, 1]]} "Class ", 1818, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 1, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 5, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[3, 5, 4, 1, 2], [1, 0, 1, 1]]} "Class ", 1819, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 1, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 5, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 5, 4, 1, 2], [0, 1, 1, 1]]} "Class ", 1820, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 1, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 5, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 2, 1, 3], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 5, 4, 1, 2], [1, 1, 1, 1]]} "Class ", 1821, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 3, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 5, 4], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 3, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 5, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}] , [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 198, 854, 4020, 20488, 112176, 655488, 4065841, 26650499, 183892324, 1331308805, 10082912861, 79683822888, 655601873235, 5604139597664, 49679530246527] "" "Class ", 1822, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 3, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 5, 4], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 3, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 5, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 197, 846, 3971, 20190, 110309, 643374, 3984326, 26079981, 179735800, 1299808808, 9834859248, 77656494812, 638426466813, 5453497161827, 48313352029786] "" "Class ", 1823, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 1, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 3, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 5, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 3, 4, 1, 2], [0, 1, 0, 0]]} "Class ", 1824, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 1, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 3, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 5, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 3, 4, 1, 2], [1, 1, 0, 0]]} "Class ", 1825, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 5, 4], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 5, 4], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 826, 3814, 19026, 101867, 581722, 3524537, 22559794, 151989996, 1074317886, 7944242775, 61303247544, 492552952894, 4112320171918, 35612010429371] "" "Class ", 1826, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 815, 3730, 18423, 97537, 550333, 3292708, 20802439, 138273906, 963968749, 7028696251, 53469233099, 423441770386, 3484046890615, 29730154573382] "" "Class ", 1827, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 1, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 5, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 3, 4, 1, 2], [0, 1, 1, 0]]} "Class ", 1828, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 1, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 5, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 3, 4, 1, 2], [1, 1, 1, 0]]} "Class ", 1829, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 3, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 5, 4], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 3, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 5, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 3}, {}], [[4, 2, 3, 1], {1, 2}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 817, 3761, 18736, 100257, 572747, 3474948, 22291394, 150616289, 1068342370, 7932055888, 61486069819, 496460094396, 4166895222361, 36287176912642] "" "Class ", 1830, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 3, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 5, 4], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 3, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 5, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {}], [[4, 2, 3, 1], {2, 3}, {[0, 1, 0, 0, 0]}], [[4, 1, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 3, 2], {3}, {}], [[5, 2, 4, 3, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 804, 3648, 17869, 93841, 525396, 3120961, 19587865, 129424249, 897436031, 6512368648, 49333593270, 389267318437, 3192887424939, 27174463343038] "" "Class ", 1831, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 1, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 3, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 5, 4], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 3, 4, 1, 2], [0, 1, 0, 1]]} "Class ", 1832, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 1, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 3, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 5, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 3, 4, 1, 2], [1, 1, 0, 1]]} "Class ", 1833, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 5, 4], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]} "Class ", 1834, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]} "Class ", 1835, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 1, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 5, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 3, 4, 1, 2], [0, 1, 1, 1]]} "Class ", 1836, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 1, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 5, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 3, 4, 1, 2], [1, 1, 1, 1]]} "Class ", 1837, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 5, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 5, 4], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 5, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 5, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [4, 5, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 199, 858, 4044, 20630, 113047, 661005, 4102403, 26903757, 185722092, 1345079695, 10190738257, 80560899139, 663002462611, 5668822780662, 50264358522242] "" "Class ", 1838, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 5, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 5, 4], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 5, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 5, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 831, 3843, 19205, 102993, 588979, 3573374, 22902192, 154486316, 1093230643, 8093018048, 62516809530, 502804344444, 4201888068327, 36420450427715] "" "Class ", 1839, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 5, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 5, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {4}, {}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {4}, {}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {4}, {}], [[3, 4, 2, 1, 5], {3}, {}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {4}, {}], [[3, 5, 2, 1, 4], {3}, {}], [[3, 5, 2, 4, 1], {2, 3}, {}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {4}, {}], [[4, 5, 2, 1, 3], {3}, {}], [[4, 5, 2, 3, 1], {3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 826, 3820, 19102, 102551, 587426, 3571277, 22942622, 155160826, 1101076272, 8175216109, 63346717612, 511104080084, 4285222365690, 37266694433419] "" "Class ", 1840, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 5, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 5, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [1, 1, 0, 0]]} "Class ", 1841, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 5, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 5, 4], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 5, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 5, 4], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [4, 5, 2, 1, 3], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 817, 3754, 18623, 99085, 562233, 3384646, 21522521, 144036394, 1011277589, 7427787953, 56931292199, 454336476444, 3767651187121, 32407441044046] "" "Class ", 1842, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 5, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 5, 4], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 782, 3467, 16492, 83609, 449397, 2549613, 15209645, 95089470, 621259549, 4231077729, 29970857297, 220370586967, 1678950952118, 13232765279988] "" "Class ", 1843, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 5, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 5, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 1, 0]]} "Class ", 1844, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 5, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 5, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [1, 1, 1, 0]]} "Class ", 1845, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 5, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 5, 4], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 5, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 5, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 826, 3826, 19192, 103460, 595619, 3642546, 23557040, 160483907, 1147825394, 8593549583, 67172163192, 546912678465, 4628661844716, 40643206332458] "" "Class ", 1846, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 5, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 5, 4], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [1, 0, 0, 1]]} "Class ", 1847, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 5, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 5, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {3}, {[0, 1, 0, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {4}, {}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {4}, {}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {4}, {}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {4}, {}], [[3, 5, 2, 4, 1], {2, 3}, {}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {4}, {[0, 0, 1, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 777, 3403, 15937, 79369, 418385, 2325177, 13576769, 83040761, 530627121, 3534012713, 24480060457, 176035052425, 1311845955625, 10115460126105] "" "Class ", 1848, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 5, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 5, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [1, 1, 0, 1]]} "Class ", 1849, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 5, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 5, 4], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 5, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 5, 4], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {3}, {[0, 1, 0, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {4}, {}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {4}, {}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {4}, {}], [[3, 4, 2, 5, 1], {1, 2}, {[0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {4}, {}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {4}, {}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 1, 0, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 779, 3436, 16283, 82421, 443515, 2527281, 15197841, 96150012, 638199237, 4433345381, 32159317603, 243107691367, 1911608865375, 15608691292650] "" "Class ", 1850, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 5, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 5, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 1]]} "Class ", 1851, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 5, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 5, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 5, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 5, 4], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {3}, {[0, 1, 0, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {4}, {}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {4}, {}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {4}, {}], [[3, 4, 2, 5, 1], {2, 3}, {[0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {4}, {}], [[3, 5, 2, 4, 1], {2, 3}, {[0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {4}, {[0, 0, 1, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 749, 3149, 13997, 65637, 324093, 1681557, 9148685, 52083509, 309639629, 1918634805, 12368650701, 82815657525, 575014148813, 4134126910517] "" "Class ", 1852, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 5, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 5, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 3, 1, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 5, 3, 1, 2], [1, 1, 1, 1]]} "Class ", 1853, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [4, 5, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 5, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 5, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 837, 3900, 19660, 106401, 614461, 3766285, 24391241, 166273511, 1189199516, 8897662825, 69467109081, 564650817794, 4768666898714, 41767236529799] "" "Class ", 1854, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 812, 3729, 18513, 98622, 560625, 3382881, 21571376, 144816179, 1020235123, 7521133741, 57871063268, 463715758085, 3861657143379, 33360429966454] "" "Class ", 1855, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 1, 4], {}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 1, 3], {}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {}, {}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {4}, {}], [[2, 5, 4, 3, 1], {1}, {}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2}, {}], [[4, 2, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {1, 2}, {}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {4}, {}], [[4, 3, 2, 1, 5], {3}, {}], [[4, 3, 2, 5, 1], {3, 4}, {}], [[5, 2, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2}, {}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {4}, {}], [[5, 3, 2, 1, 4], {3}, {}], [[5, 3, 2, 4, 1], {3, 4}, {}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {4}, {}], [[5, 4, 2, 1, 3], {3}, {}], [[5, 4, 2, 3, 1], {3}, {}], [[5, 4, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 802, 3651, 17959, 94716, 532844, 3180867, 20062339, 133205435, 928078390, 6766167786, 51488148184, 408044678655, 3361025330667, 28721712620547] "" "Class ", 1856, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 5, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [1, 1, 0, 0]]} "Class ", 1857, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 5, 4], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 5, 4], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [4, 5, 2, 1, 3], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 5, 3, 1, 2], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 5, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 795, 3579, 17316, 89600, 492820, 2868288, 17592138, 113325476, 764390580, 5384522185, 39518018728, 301543575744, 2387748398221, 19587041751271] "" "Class ", 1858, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 767, 3372, 15897, 79874, 425572, 2393895, 14162683, 87835172, 569424747, 3849104210, 27068829567, 197650815851, 1495776974288, 11713003722032] "" "Class ", 1859, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 5, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 1, 0]]} "Class ", 1860, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 5, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]} "Class ", 1861, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {[0, 0, 1, 0, 0, 0]}], [[2, 5, 4, 3, 1], {1, 2}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 792, 3535, 16914, 86166, 464497, 2636341, 15689680, 97557827, 631845006, 4251208396, 29645060247, 213813263409, 1592082305098, 12218890953967] "" "Class ", 1862, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {3}, {[0, 0, 1, 0, 0, 0]}], [[2, 5, 4, 3, 1], {1, 3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 1, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 3, 2], {3}, {[0, 0, 1, 0, 0, 0]}], [[5, 2, 4, 3, 1], {2, 3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 753, 3191, 14264, 66837, 326622, 1657807, 8709763, 47231022, 263725171, 1513156426, 8905320748, 53675059400, 330869939739, 2083414782811] "" "Class ", 1863, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 1, 4], {}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 1, 3], {}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {3}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {4}, {[0, 0, 1, 0, 0, 0]}], [[2, 5, 4, 3, 1], {1, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2}, {}], [[4, 2, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {1, 2}, {}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {4}, {}], [[4, 3, 2, 5, 1], {3, 4}, {}], [[5, 2, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2}, {}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {4}, {}], [[5, 3, 2, 4, 1], {3, 4}, {}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {4}, {[0, 0, 1, 0, 0, 0]}], [[5, 4, 2, 3, 1], {3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 739, 3065, 13321, 60340, 283647, 1378917, 6912447, 35645393, 188693135, 1023570136, 5680889655, 32215369042, 186438947401, 1099949032050] "" "Class ", 1864, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 5, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]} "Class ", 1865, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 5, 4], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]} "Class ", 1866, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 5, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]} "Class ", 1867, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 5, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 1, 1]]} "Class ", 1868, " is:" {{[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 5, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[4, 5, 3, 2, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]} "Class ", 1869, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 2, 3, 4], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 4, 5, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 4, 3, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 2, 1, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 2, 3, 4], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 3, 4, 5, 1], [0, 1, 1, 0]]} "Class ", 1870, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 2, 3, 4], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 4, 5, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 4, 3, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 2, 1, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 2, 3, 4], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 3, 4, 5, 1], [1, 1, 1, 0]]} "Class ", 1871, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 4, 5, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 2, 1, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 3, 4, 5, 1], [0, 1, 1, 1]]} "Class ", 1872, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 4, 5, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 3, 4, 5, 1], [1, 1, 1, 1]]} "Class ", 1873, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 2, 4, 3], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 4, 5, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 4, 2, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 2, 1, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 2, 4, 3], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 2, 4, 5, 1], [0, 0, 1, 0]]} "Class ", 1874, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 2, 4, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 4, 5, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 4, 2, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 2, 1, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 2, 4, 3], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[3, 2, 4, 5, 1], [1, 0, 1, 0]]} "Class ", 1875, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 2, 4, 3], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 4, 5, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 4, 2, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 2, 1, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 2, 4, 3], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 2, 4, 5, 1], [0, 1, 1, 0]]} "Class ", 1876, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 2, 4, 3], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 4, 5, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 4, 2, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 2, 1, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 2, 4, 3], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 2, 4, 5, 1], [1, 1, 1, 0]]} "Class ", 1877, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 4, 5, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 2, 1, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 2, 4, 5, 1], [0, 0, 1, 1]]} "Class ", 1878, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 4, 5, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 2, 1, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[3, 2, 4, 5, 1], [1, 0, 1, 1]]} "Class ", 1879, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 4, 5, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 2, 1, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 2, 4, 5, 1], [0, 1, 1, 1]]} "Class ", 1880, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 4, 5, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 2, 1, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 2, 4, 5, 1], [1, 1, 1, 1]]} "Class ", 1881, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 3, 2, 4], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 3, 5, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 3, 4, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 3, 1, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 3, 2, 4], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 4, 3, 5, 1], [0, 0, 1, 0]]} "Class ", 1882, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 3, 2, 4], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 3, 5, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 3, 4, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 3, 1, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 3, 2, 4], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[2, 4, 3, 5, 1], [1, 0, 1, 0]]} "Class ", 1883, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 3, 2, 4], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 3, 5, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 3, 4, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 3, 1, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 3, 2, 4], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 4, 3, 5, 1], [0, 1, 1, 0]]} "Class ", 1884, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 3, 2, 4], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 3, 5, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 3, 4, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 3, 1, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 3, 2, 4], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 4, 3, 5, 1], [1, 1, 1, 0]]} "Class ", 1885, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 3, 5, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 3, 1, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 4, 3, 5, 1], [0, 0, 1, 1]]} "Class ", 1886, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 3, 5, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 3, 1, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[2, 4, 3, 5, 1], [1, 0, 1, 1]]} "Class ", 1887, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 3, 5, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 3, 1, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 4, 3, 5, 1], [0, 1, 1, 1]]} "Class ", 1888, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 3, 5, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 3, 1, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 4, 3, 5, 1], [1, 1, 1, 1]]} "Class ", 1889, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 3, 4, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 3, 5, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 3, 2, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 3, 1, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 3, 4, 2], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 2, 3, 5, 1], [0, 0, 1, 0]]} "Class ", 1890, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 3, 4, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 3, 5, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 3, 2, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 3, 1, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 3, 4, 2], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 2, 3, 5, 1], [1, 0, 1, 0]]} "Class ", 1891, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 3, 4, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 3, 5, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 3, 2, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 3, 1, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 3, 4, 2], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 2, 3, 5, 1], [0, 1, 1, 0]]} "Class ", 1892, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 3, 4, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 3, 5, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 3, 2, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 3, 1, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 3, 4, 2], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 2, 3, 5, 1], [1, 1, 1, 0]]} "Class ", 1893, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 3, 5, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 3, 1, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 2, 3, 5, 1], [0, 0, 1, 1]]} "Class ", 1894, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 3, 5, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 3, 1, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 2, 3, 5, 1], [1, 0, 1, 1]]} "Class ", 1895, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 3, 5, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 3, 1, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 2, 3, 5, 1], [0, 1, 1, 1]]} "Class ", 1896, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 3, 5, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 3, 1, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 2, 3, 5, 1], [1, 1, 1, 1]]} "Class ", 1897, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 818, 3776, 18898, 101728, 585047, 3575238, 23109906, 157384392, 1125421442, 8424872889, 65851128446, 536165966315, 4537981248178, 39850655221467] "" "Class ", 1898, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 1, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 1, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 793, 3562, 17262, 89684, 496894, 2922141, 18165176, 118937554, 817644030, 5885082985, 44237620651, 346498959821, 2822275646421, 23860709047645] "" "Class ", 1899, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 5, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 1, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 4, 2, 5, 1], [0, 1, 0, 0]]} "Class ", 1900, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 5, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 1, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 4, 2, 5, 1], [1, 1, 0, 0]]} "Class ", 1901, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 4, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 1, 0]]} "Class ", 1902, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 4, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 1, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 0]]} "Class ", 1903, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 5, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 4, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 1, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 4, 2, 5, 1], [0, 1, 1, 0]]} "Class ", 1904, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 4, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 1, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 0]]} "Class ", 1905, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 3, 2], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 2, 4, 3, 1], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 780, 3452, 16459, 84106, 458526, 2655754, 16277693, 105201234, 714608624, 5087138326, 37853172665, 293720171174, 2371633811350, 19888906780633] "" "Class ", 1906, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 1, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 1, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 748, 3130, 13775, 63545, 306455, 1541401, 8067767, 43849073, 246993312, 1439303088, 8662880822, 53775647940, 343836778725, 2261741753191] "" "Class ", 1907, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 5, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 1, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 1, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 5, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 1, 5], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 3, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 2, 4, 3, 1], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [5, 3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 748, 3128, 13731, 62969, 300552, 1488704, 7634723, 40464741, 221311617, 1247444859, 7238458309, 43196661875, 264878725516, 1667564565616] "" "Class ", 1908, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 5, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 1, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 5, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 1, 5], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [5, 3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 731, 2950, 12235, 51822, 223191, 974427, 4302645, 19181100, 86211885, 390248055, 1777495635, 8140539950, 37463689775, 173164232965] "" "Class ", 1909, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 1, 1]]} "Class ", 1910, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 1, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 1]]} "Class ", 1911, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 5, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 1, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 4, 2, 5, 1], [0, 1, 1, 1]]} "Class ", 1912, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 4, 1, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 1]]} "Class ", 1913, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 3, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 1, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 3, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 1, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 1, 4, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 805, 3664, 18033, 95274, 537188, 3216209, 20358002, 135725244, 949938251, 6959614406, 53237382713, 424224671246, 3514233289517, 30207532875623] "" "Class ", 1914, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 5, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 3, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 1, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 5, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 3, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 1, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 780, 3455, 16508, 84602, 462687, 2688153, 16524205, 107079079, 729113152, 5201580953, 38779570913, 301431829310, 2437721123881, 20472186451417] "" "Class ", 1915, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 5, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 3, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 1, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 3, 2, 5, 1], [0, 1, 0, 0]]} "Class ", 1916, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 5, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 3, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 1, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 3, 2, 5, 1], [1, 1, 0, 0]]} "Class ", 1917, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 5, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 3, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 1, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 3, 2, 5, 1], [0, 0, 1, 0]]} "Class ", 1918, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 5, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 3, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 1, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 3, 2, 5, 1], [1, 0, 1, 0]]} "Class ", 1919, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 5, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 3, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 1, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 3, 2, 5, 1], [0, 1, 1, 0]]} "Class ", 1920, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 5, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 3, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 1, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 3, 2, 5, 1], [1, 1, 1, 0]]} "Class ", 1921, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 1, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 1, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 1, 4, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 3, 1], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 763, 3273, 14910, 71825, 364628, 1944877, 10868953, 63472290, 386358127, 2445600821, 16063217292, 109264401391, 768344051665, 5576640236784] "" "Class ", 1922, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 5, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 1, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 5, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 1, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 731, 2950, 12235, 51822, 223191, 974427, 4302645, 19181100, 86211885, 390248055, 1777495635, 8140539950, 37463689775, 173164232965] "" "Class ", 1923, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 5, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 1, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 3, 2, 5, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 5, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 1, 5], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[4, 3, 2, 5, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {3}, {}], [[3, 2, 1, 4], {1, 2}, {[1, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 1, 3], {1}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {1}, {}], [[4, 3, 2, 1], {1}, {}], [[3, 2, 4, 1, 5], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {2, 3}, {}], [[4, 3, 5, 1, 2], {2, 3}, {}], [[4, 3, 5, 2, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 187, 718, 2846, 11564, 47952, 202214, 864710, 3740953, 16344182, 72011453, 319603580, 1427576121, 6412671901, 28950671615, 131288988431] "" "Class ", 1924, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 5, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 1, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 5, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 1, 5], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 1, 4, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 2, 4, 3, 1], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [ [5, 3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 186, 701, 2677, 10269, 39438, 151477, 581727, 2233751, 8576598, 32928917, 126424709, 485381785, 1863519946, 7154584645, 27468492959] "" "Class ", 1925, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 5, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 1, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 3, 2, 5, 1], [0, 0, 1, 1]]} "Class ", 1926, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 5, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 1, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 3, 2, 5, 1], [1, 0, 1, 1]]} "Class ", 1927, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 5, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 1, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 3, 2, 5, 1], [0, 1, 1, 1]]} "Class ", 1928, " is:" {{[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 2, 5, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 4, 1, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 3, 2, 5, 1], [1, 1, 1, 1]]} "Class ", 1929, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 1, 3, 4], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 5, 4, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 5, 3, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 1, 2, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 1, 3, 4], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 3, 5, 4, 1], [0, 1, 0, 0]]} "Class ", 1930, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 1, 3, 4], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 5, 4, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 5, 3, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 1, 2, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 1, 3, 4], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 3, 5, 4, 1], [1, 1, 0, 0]]} "Class ", 1931, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 1, 3, 4], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 5, 4, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 5, 3, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 1, 2, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 1, 3, 4], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 3, 5, 4, 1], [0, 1, 1, 0]]} "Class ", 1932, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 1, 3, 4], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 5, 4, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 5, 3, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 1, 2, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 1, 3, 4], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 3, 5, 4, 1], [1, 1, 1, 0]]} "Class ", 1933, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 5, 4, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 1, 2, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 3, 5, 4, 1], [0, 1, 0, 1]]} "Class ", 1934, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 5, 4, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 1, 2, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 3, 5, 4, 1], [1, 1, 0, 1]]} "Class ", 1935, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 5, 4, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 1, 2, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 3, 5, 4, 1], [0, 1, 1, 1]]} "Class ", 1936, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 5, 4, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 3, 1, 2, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 3, 5, 4, 1], [1, 1, 1, 1]]} "Class ", 1937, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 4, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 5, 2, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 4, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 5, 2, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [[4, 2, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 803, 3635, 17756, 92947, 518448, 3066672, 19157123, 125932959, 868424833, 6264789123, 47162101202, 369688219550, 3011427855680, 25446263943047] "" "Class ", 1938, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 4, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 5, 2, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 2, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 4, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 5, 2, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 2, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 778, 3425, 16207, 82004, 441501, 2518500, 15165427, 96084584, 638658352, 4441778613, 32247001661, 243858600281, 1917175955900, 15642091510245] "" "Class ", 1939, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 4, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 5, 2, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 2, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 2, 5, 4, 1], [0, 1, 0, 0]]} "Class ", 1940, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 4, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 5, 2, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 2, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 2, 5, 4, 1], [1, 1, 0, 0]]} "Class ", 1941, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 4, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 5, 2, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 2, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 2, 5, 4, 1], [0, 0, 1, 0]]} "Class ", 1942, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 4, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 5, 2, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 2, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[3, 2, 5, 4, 1], [1, 0, 1, 0]]} "Class ", 1943, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 4, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 5, 2, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 2, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 2, 5, 4, 1], [0, 1, 1, 0]]} "Class ", 1944, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 4, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 5, 2, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 2, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 2, 5, 4, 1], [1, 1, 1, 0]]} "Class ", 1945, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 4, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 4, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {2}, {}], [[4, 2, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 776, 3383, 15703, 77161, 399526, 2171586, 12350814, 73296365, 452752719, 2904492897, 19312842565, 132864469863, 944173893066, 6920442667182] "" "Class ", 1946, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 4, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 2, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 4, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 2, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 747, 3111, 13551, 61419, 288543, 1400727, 7008519, 36065919, 190531623, 1031674935, 5717624727, 32392623783, 187392817623, 1105868383095] "" "Class ", 1947, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 4, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 2, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 2, 5, 4, 1], [0, 1, 0, 1]]} "Class ", 1948, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 4, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 2, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 2, 5, 4, 1], [1, 1, 0, 1]]} "Class ", 1949, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 4, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 2, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 2, 5, 4, 1], [0, 0, 1, 1]]} "Class ", 1950, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 4, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 2, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[3, 2, 5, 4, 1], [1, 0, 1, 1]]} "Class ", 1951, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 4, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 2, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 2, 5, 4, 1], [0, 1, 1, 1]]} "Class ", 1952, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 5, 4, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 4, 1, 2, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 2, 5, 4, 1], [1, 1, 1, 1]]} "Class ", 1953, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 3, 1, 4], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 3, 4, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 3, 5, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 3, 2, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 3, 1, 4], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 5, 3, 4, 1], [0, 0, 1, 0]]} "Class ", 1954, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 3, 1, 4], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 3, 4, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 3, 5, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 3, 2, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 3, 1, 4], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[2, 5, 3, 4, 1], [1, 0, 1, 0]]} "Class ", 1955, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 3, 1, 4], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 3, 4, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 3, 5, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 3, 2, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 3, 1, 4], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 5, 3, 4, 1], [0, 1, 1, 0]]} "Class ", 1956, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 3, 1, 4], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 3, 4, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 3, 5, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 3, 2, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 3, 1, 4], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 5, 3, 4, 1], [1, 1, 1, 0]]} "Class ", 1957, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 3, 1, 4], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 3, 4, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 3, 2, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 3, 1, 4], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 5, 3, 4, 1], [0, 0, 1, 1]]} "Class ", 1958, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 3, 1, 4], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 3, 4, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 3, 2, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 3, 1, 4], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[2, 5, 3, 4, 1], [1, 0, 1, 1]]} "Class ", 1959, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 3, 1, 4], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 3, 4, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 3, 2, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 3, 1, 4], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 5, 3, 4, 1], [0, 1, 1, 1]]} "Class ", 1960, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 3, 1, 4], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 3, 4, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 3, 2, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 3, 1, 4], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 5, 3, 4, 1], [1, 1, 1, 1]]} "Class ", 1961, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 3, 4, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 3, 4, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 3, 2, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 3, 2, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 3, 4, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 2, 3, 4, 1], [0, 0, 1, 0]]} "Class ", 1962, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 3, 4, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 3, 4, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 3, 2, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 3, 2, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 3, 4, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 2, 3, 4, 1], [1, 0, 1, 0]]} "Class ", 1963, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 3, 4, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 3, 4, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 3, 2, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 3, 2, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 3, 4, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 2, 3, 4, 1], [0, 1, 1, 0]]} "Class ", 1964, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 3, 4, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 3, 4, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 3, 2, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 3, 2, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 3, 4, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 2, 3, 4, 1], [1, 1, 1, 0]]} "Class ", 1965, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 3, 4, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 3, 4, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 3, 2, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 3, 4, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 2, 3, 4, 1], [0, 0, 1, 1]]} "Class ", 1966, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 3, 4, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 3, 4, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 3, 2, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 3, 4, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 2, 3, 4, 1], [1, 0, 1, 1]]} "Class ", 1967, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 3, 4, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 3, 4, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 3, 2, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 3, 4, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 2, 3, 4, 1], [0, 1, 1, 1]]} "Class ", 1968, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 3, 4, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 3, 4, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 3, 2, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 3, 4, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 2, 3, 4, 1], [1, 1, 1, 1]]} "Class ", 1969, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 4, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 5, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 2, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 4, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 5, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 2, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 819, 3787, 18977, 102242, 588387, 3597529, 23264202, 158493888, 1133707074, 8489124759, 66368222910, 540480881275, 4575272733737, 40184061800942] "" "Class ", 1970, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 4, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 5, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 2, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 4, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 5, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 2, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 807, 3688, 18240, 96918, 549920, 3314685, 21130423, 141919046, 1000902447, 7390745119, 56990574349, 457858086813, 3824455221696, 33151641005160] "" "Class ", 1971, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 4, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 5, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 2, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 5, 2, 4, 1], [0, 1, 0, 0]]} "Class ", 1972, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 4, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 5, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 2, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 5, 2, 4, 1], [1, 1, 0, 0]]} "Class ", 1973, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 4, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 5, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 2, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 5, 2, 4, 1], [0, 0, 1, 0]]} "Class ", 1974, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 4, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 5, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 2, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[3, 5, 2, 4, 1], [1, 0, 1, 0]]} "Class ", 1975, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 4, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 5, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 2, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 5, 2, 4, 1], [0, 1, 1, 0]]} "Class ", 1976, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 4, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 5, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 2, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 5, 2, 4, 1], [1, 1, 1, 0]]} "Class ", 1977, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 4, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 5, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 2, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 4, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 5, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 2, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 3, 4, 2, 1], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 795, 3594, 17593, 92599, 520950, 3116245, 19730396, 131705338, 923734756, 6786715957, 52093508014, 416762789068, 3467788321705, 29953169244046] "" "Class ", 1978, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 4, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 5, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 2, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 4, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 5, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 2, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 781, 3468, 16615, 85350, 467660, 2721089, 16745603, 108604036, 739939724, 5281062362, 39383693745, 306186987867, 2476470104486, 20798888387482] "" "Class ", 1979, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 4, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 5, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 2, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 5, 2, 4, 1], [0, 1, 0, 1]]} "Class ", 1980, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 4, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 5, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 2, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 5, 2, 4, 1], [1, 1, 0, 1]]} "Class ", 1981, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 4, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 5, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 2, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 5, 2, 4, 1], [0, 0, 1, 1]]} "Class ", 1982, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 4, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 5, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 2, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[3, 5, 2, 4, 1], [1, 0, 1, 1]]} "Class ", 1983, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 4, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 5, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 2, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 5, 2, 4, 1], [0, 1, 1, 1]]} "Class ", 1984, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 2, 4, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 5, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 4, 2, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 4, 1, 3], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 5, 2, 4, 1], [1, 1, 1, 1]]} "Class ", 1985, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 4, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 3, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 2, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 4, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 3, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 2, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 1, 4, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 2, 4, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 808, 3708, 18451, 98704, 564018, 3424291, 21986932, 148720189, 1056141006, 7851241309, 60937604371, 492668906335, 4140433464631, 36103140542930] "" "Class ", 1986, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 4, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 3, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 2, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 4, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 3, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 2, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}] , [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 781, 3469, 16633, 85544, 469365, 2734929, 16855233, 109471596, 746878094, 5337545567, 39853886524, 310200033573, 2511636127239, 21115499161691] "" "Class ", 1987, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 4, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 3, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 2, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 3, 2, 4, 1], [0, 1, 0, 0]]} "Class ", 1988, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 4, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 3, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 2, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 3, 2, 4, 1], [1, 1, 0, 0]]} "Class ", 1989, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 4, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 3, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 2, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 3, 2, 4, 1], [0, 0, 1, 0]]} "Class ", 1990, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 4, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 3, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 2, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 3, 2, 4, 1], [1, 0, 1, 0]]} "Class ", 1991, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 4, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 3, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 2, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 3, 2, 4, 1], [0, 1, 1, 0]]} "Class ", 1992, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 4, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 3, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 2, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 3, 2, 4, 1], [1, 1, 1, 0]]} "Class ", 1993, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 4, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 3, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 2, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 4, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 3, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 2, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 1, 4, 3, 2], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 2, 4, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 781, 3475, 16741, 86721, 479723, 2817907, 17498557, 114446889, 785785929, 5647147005, 42369624845, 331123450893, 2689992034673, 22674580334383] "" "Class ", 1994, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 4, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 3, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 2, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 4, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 3, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 2, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}] , [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 748, 3130, 13775, 63545, 306455, 1541401, 8067767, 43849073, 246993312, 1439303088, 8662880822, 53775647940, 343836778725, 2261741753191] "" "Class ", 1995, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 4, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 3, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 2, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 3, 2, 4, 1], [0, 1, 0, 1]]} "Class ", 1996, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 4, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 3, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 2, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [1, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 4, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 3, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 2, 5], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}] , [[4, 2, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {1, 2}, { [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 187, 719, 2869, 11865, 50931, 227193, 1053201, 5068909, 25292743, 130655763, 697812509, 3848651891, 21895557199, 128356870599, 774556194325] "" "Class ", 1997, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 4, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 2, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 3, 2, 4, 1], [0, 0, 1, 1]]} "Class ", 1998, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 4, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 2, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 3, 2, 4, 1], [1, 0, 1, 1]]} "Class ", 1999, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 4, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 2, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 3, 2, 4, 1], [0, 1, 1, 1]]} "Class ", 2000, " is:" {{[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 2, 4, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 4, 2, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 2, 4, 3, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 3, 2, 4, 1], [1, 1, 1, 1]]} "Class ", 2001, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 1, 2, 4], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 5, 3, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 5, 4, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 1, 3, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 1, 2, 4], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 4, 5, 3, 1], [0, 1, 0, 0]]} "Class ", 2002, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 1, 2, 4], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 5, 3, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 5, 4, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 1, 3, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 1, 2, 4], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 4, 5, 3, 1], [1, 1, 0, 0]]} "Class ", 2003, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 1, 2, 4], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 5, 3, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 5, 4, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 1, 3, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 1, 2, 4], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 4, 5, 3, 1], [0, 1, 1, 0]]} "Class ", 2004, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 1, 2, 4], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 5, 3, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 5, 4, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 1, 3, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 1, 2, 4], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 4, 5, 3, 1], [1, 1, 1, 0]]} "Class ", 2005, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 1, 2, 4], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 5, 3, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 5, 4, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 1, 3, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 1, 2, 4], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 4, 5, 3, 1], [0, 1, 0, 1]]} "Class ", 2006, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 1, 2, 4], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 5, 3, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 5, 4, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 1, 3, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 1, 2, 4], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 4, 5, 3, 1], [1, 1, 0, 1]]} "Class ", 2007, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 1, 2, 4], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 5, 3, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 1, 3, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 1, 2, 4], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 4, 5, 3, 1], [0, 1, 1, 1]]} "Class ", 2008, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 1, 2, 4], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 4, 5, 3, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 2, 1, 3, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 1, 2, 4], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 4, 5, 3, 1], [1, 1, 1, 1]]} "Class ", 2009, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 3, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 5, 2, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 3, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 3, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 5, 2, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 3, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [[4, 2, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 805, 3669, 18106, 95979, 543052, 3262742, 20725144, 138653982, 973743480, 7157676626, 54928797753, 439070941603, 3648242762315, 31451574392269] "" "Class ", 2010, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 3, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 5, 2, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 3, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 3, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 5, 2, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 3, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 778, 3425, 16207, 82004, 441501, 2518500, 15165427, 96084584, 638658352, 4441778613, 32247001661, 243858600281, 1917175955900, 15642091510245] "" "Class ", 2011, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 3, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 5, 2, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 3, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 2, 5, 3, 1], [0, 1, 0, 0]]} "Class ", 2012, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 3, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 5, 2, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 3, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 2, 5, 3, 1], [1, 1, 0, 0]]} "Class ", 2013, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 3, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 5, 2, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 3, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 2, 5, 3, 1], [0, 0, 1, 0]]} "Class ", 2014, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 3, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 5, 2, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 3, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 2, 5, 3, 1], [1, 0, 1, 0]]} "Class ", 2015, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 3, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 5, 2, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 3, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 2, 5, 3, 1], [0, 1, 1, 0]]} "Class ", 2016, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 3, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 5, 2, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 3, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 2, 5, 3, 1], [1, 1, 1, 0]]} "Class ", 2017, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 3, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 5, 2, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 3, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 3, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 5, 2, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 3, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {2}, {}], [[4, 2, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 792, 3555, 17244, 89768, 498435, 2936753, 18283073, 119831464, 824213939, 5932284533, 44567914205, 348711919868, 2835838843416, 23926354003601] "" "Class ", 2018, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 3, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 5, 2, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 3, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 3, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 5, 2, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 3, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 762, 3257, 14734, 70164, 350173, 1824916, 9900831, 55776020, 325541041, 1964740513, 12240641505, 78603636042, 519551554402, 3530432003317] "" "Class ", 2019, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 3, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 5, 2, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 3, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 2, 5, 3, 1], [0, 1, 0, 1]]} "Class ", 2020, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 3, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 5, 2, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 3, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 2, 5, 3, 1], [1, 1, 0, 1]]} "Class ", 2021, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 3, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 3, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 2, 5, 3, 1], [0, 0, 1, 1]]} "Class ", 2022, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 3, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 3, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 2, 5, 3, 1], [1, 0, 1, 1]]} "Class ", 2023, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 3, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 3, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 2, 5, 3, 1], [0, 1, 1, 1]]} "Class ", 2024, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 2, 5, 3, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 4, 1, 3, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 1, 4, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 2, 5, 3, 1], [1, 1, 1, 1]]} "Class ", 2025, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 3, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 5, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 3, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 3, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 5, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 3, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [4, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {}, {}], [[4, 3, 2, 1, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[5, 3, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}] , [[5, 4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 802, 3615, 17542, 91027, 502275, 2934022, 18071797, 116971182, 793259435, 5621599367, 41533742239, 319248740699, 2548128875882, 21083141400865] "" "Class ", 2026, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 3, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 3, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 3, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 3, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [4, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 777, 3395, 15835, 78271, 408051, 2234667, 12803435, 76524755, 475820211, 3070157531, 20515518747, 141700045675, 1009905638875, 7415991261371] "" "Class ", 2027, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 3, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 5, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 3, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 5, 4, 3, 1], [0, 1, 0, 0]]} "Class ", 2028, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 3, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 5, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 3, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 5, 4, 3, 1], [1, 1, 0, 0]]} "Class ", 2029, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 3, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 5, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 3, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 5, 4, 3, 1], [0, 0, 1, 0]]} "Class ", 2030, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 3, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 5, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 3, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[2, 5, 4, 3, 1], [1, 0, 1, 0]]} "Class ", 2031, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 3, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 5, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 3, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 5, 4, 3, 1], [0, 1, 1, 0]]} "Class ", 2032, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 3, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 5, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 3, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 5, 4, 3, 1], [1, 1, 1, 0]]} "Class ", 2033, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 3, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 3, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 3, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 3, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [4, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {}, {}], [[4, 3, 2, 1, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[5, 3, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}] , [[5, 4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 789, 3495, 16545, 83142, 441009, 2457963, 14339835, 87281820, 552702609, 3632275683, 24719681601, 173880087210, 1261984254525, 9435921363783] "" "Class ", 2034, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 3, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 3, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 3, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 3, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [4, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 777, 3395, 15835, 78271, 408051, 2234667, 12803435, 76524755, 475820211, 3070157531, 20515518747, 141700045675, 1009905638875, 7415991261371] "" "Class ", 2035, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 3, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 3, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 5, 4, 3, 1], [0, 1, 0, 1]]} "Class ", 2036, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 3, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 3, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 5, 4, 3, 1], [1, 1, 0, 1]]} "Class ", 2037, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 3, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 3, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 5, 4, 3, 1], [0, 0, 1, 1]]} "Class ", 2038, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 3, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 3, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[2, 5, 4, 3, 1], [1, 0, 1, 1]]} "Class ", 2039, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 3, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 3, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 5, 4, 3, 1], [0, 1, 1, 1]]} "Class ", 2040, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 5, 4, 3, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[4, 1, 2, 3, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 5, 4, 3, 1], [1, 1, 1, 1]]} "Class ", 2041, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 3, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 2, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 3, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 3, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 2, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 3, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [[4, 2, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 3, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 808, 3708, 18452, 98721, 564210, 3426163, 22004052, 148872728, 1057495145, 7863372697, 61048016101, 493693579066, 4150152300944, 36197480404241] "" "Class ", 2042, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 3, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 2, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 3, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 3, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 2, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 3, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 778, 3425, 16207, 82004, 441501, 2518500, 15165427, 96084584, 638658352, 4441778613, 32247001661, 243858600281, 1917175955900, 15642091510245] "" "Class ", 2043, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 3, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 2, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 3, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 2, 4, 3, 1], [0, 1, 0, 0]]} "Class ", 2044, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 3, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 2, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 3, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 2, 4, 3, 1], [1, 1, 0, 0]]} "Class ", 2045, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 3, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 2, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 3, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 2, 4, 3, 1], [0, 0, 1, 0]]} "Class ", 2046, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 3, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 2, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 3, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 2, 4, 3, 1], [1, 0, 1, 0]]} "Class ", 2047, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 3, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 2, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 3, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 2, 4, 3, 1], [0, 1, 1, 0]]} "Class ", 2048, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 3, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 2, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 3, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 2, 4, 3, 1], [1, 1, 1, 0]]} "Class ", 2049, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 3, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 2, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 3, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 3, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 2, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 3, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {2}, {}], [[4, 2, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 3, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 795, 3598, 17647, 93040, 523908, 3134462, 19835541, 132250198, 925862185, 6785977582, 51935514799, 414090854400, 3432447953422, 29524127400678] "" "Class ", 2050, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 3, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 2, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 3, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 3, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 2, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 3, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 762, 3257, 14734, 70164, 350173, 1824916, 9900831, 55776020, 325541041, 1964740513, 12240641505, 78603636042, 519551554402, 3530432003317] "" "Class ", 2051, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 3, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 2, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 3, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 2, 4, 3, 1], [0, 1, 0, 1]]} "Class ", 2052, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 3, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 2, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 3, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 2, 4, 3, 1], [1, 1, 0, 1]]} "Class ", 2053, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 3, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 3, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 2, 4, 3, 1], [0, 0, 1, 1]]} "Class ", 2054, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 3, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 3, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 2, 4, 3, 1], [1, 0, 1, 1]]} "Class ", 2055, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 3, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 3, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 2, 4, 3, 1], [0, 1, 1, 1]]} "Class ", 2056, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 2, 4, 3, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 4, 2, 3, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 2, 4, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 2, 4, 3, 1], [1, 1, 1, 1]]} "Class ", 2057, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 5, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 3, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 5, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 3, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 3, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 831, 3887, 19715, 107505, 626069, 3872531, 25324239, 174394109, 1260386521, 9531589609, 75228809635, 618237743853, 5279360979275, 46757811295007] "" "Class ", 2058, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 3, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 5, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 3, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 3, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 5, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 3, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 806, 3676, 18147, 96278, 545589, 3284991, 20921651, 140404227, 989530036, 7302336185, 56278854141, 451927473159, 3773340145222, 32696361672450] "" "Class ", 2059, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 5, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]} "Class ", 2060, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 3, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 5, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 3, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 5, 2, 3, 1], [1, 1, 0, 0]]} "Class ", 2061, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 3, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 5, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 3, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 5, 2, 3, 1], [0, 0, 1, 0]]} "Class ", 2062, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 3, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 5, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 3, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 5, 2, 3, 1], [1, 0, 1, 0]]} "Class ", 2063, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 5, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 3, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 1, 0]]} "Class ", 2064, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 3, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 5, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 3, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 5, 2, 3, 1], [1, 1, 1, 0]]} "Class ", 2065, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 3, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 3, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 3, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 821, 3820, 19310, 105068, 610962, 3774949, 24665575, 169748676, 1226187383, 9269154747, 73132963709, 600846706818, 5129656759733, 45422964146988] "" "Class ", 2066, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 3, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 3, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 3, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 3, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 793, 3562, 17262, 89684, 496894, 2922141, 18165176, 118937554, 817644030, 5885082985, 44237620651, 346498959821, 2822275646421, 23860709047645] "" "Class ", 2067, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 1, 4, 3, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 2, 4, 3, 1], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 3, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 781, 3469, 16631, 85491, 468537, 2724833, 16747171, 108389911, 736382213, 5236791237, 38885666991, 300817541531, 2419516810609, 20196271982281] "" "Class ", 2068, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 3, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 3, 5], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 1, 4, 3, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 4, 3, 1], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 764, 3288, 15043, 72745, 370099, 1973584, 10996665, 63849977, 385410533, 2413453066, 15649413365, 104900449698, 725810507872, 5176569085801] "" "Class ", 2069, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 3, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 5, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 3, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 5, 2, 3, 1], [0, 0, 1, 1]]} "Class ", 2070, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 3, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 5, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 3, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[4, 5, 2, 3, 1], [1, 0, 1, 1]]} "Class ", 2071, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 5, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 3, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]} "Class ", 2072, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 2, 3, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 5, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 4, 3, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 5, 2, 3, 1], [1, 1, 1, 1]]} "Class ", 2073, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 3, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 4, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 3, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 3, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 4, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 3, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [5, 3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 3, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 808, 3706, 18423, 98456, 562131, 3410407, 21884107, 147944050, 1050130310, 7803282125, 60542681784, 489311676445, 4110975576423, 35836465738900] "" "Class ", 2074, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 4, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 3, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 4, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 3, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 786, 3541, 17305, 90983, 511446, 3057676, 19351431, 129132357, 905445883, 6650903708, 51041887784, 408288207111, 3396841931310, 29337187575614] "" "Class ", 2075, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 4, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 3, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]} "Class ", 2076, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 3, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 4, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 3, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 4, 2, 3, 1], [1, 1, 0, 0]]} "Class ", 2077, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 3, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 4, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 3, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 4, 2, 3, 1], [0, 0, 1, 0]]} "Class ", 2078, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 3, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 4, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 3, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 4, 2, 3, 1], [1, 0, 1, 0]]} "Class ", 2079, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 4, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 3, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 1, 0]]} "Class ", 2080, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 3, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 4, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 3, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 4, 2, 3, 1], [1, 1, 1, 0]]} "Class ", 2081, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 3, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 3, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 3, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 3, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [5, 3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 3, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 795, 3598, 17647, 93040, 523908, 3134462, 19835541, 132250198, 925862185, 6785977582, 51935514799, 414090854400, 3432447953422, 29524127400678] "" "Class ", 2082, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 3, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 3, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 770, 3390, 16133, 82440, 449784, 2608009, 16005113, 103567372, 704307166, 5018904416, 37379442425, 290280124037, 2345559494332, 19683042492399] "" "Class ", 2083, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 1, 4, 3, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 2, 4, 3, 1], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [5, 3, 4, 1, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 3, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 755, 3240, 14872, 72636, 375682, 2049509, 11753710, 70648553, 443893071, 2908473977, 19830604064, 140428353632, 1031013083778, 7835630190420] "" "Class ", 2084, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[4, 1, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 1, 4, 3, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 2, 4, 3, 1], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0]}], [ [5, 3, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 740, 3100, 13781, 64736, 319976, 1658310, 8985193, 50768670, 298448481, 1821555846, 11521295360, 75389943923, 509582981302, 3553037478863] "" "Class ", 2085, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 3, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 3, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 4, 2, 3, 1], [0, 0, 1, 1]]} "Class ", 2086, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 3, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 3, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 0]], [[5, 4, 2, 3, 1], [1, 0, 1, 1]]} "Class ", 2087, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 3, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 1, 1]]} "Class ", 2088, " is:" {{[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 2, 3, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 4, 3, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 4, 2, 3, 1], [1, 1, 1, 1]]} "Class ", 2089, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 1, 2, 3], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 5, 4, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 1, 4, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 1, 2, 3], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 0, 0]]} "Class ", 2090, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 1, 2, 3], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 5, 4, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 1, 4, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 1, 2, 3], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 0, 0]]} "Class ", 2091, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 1, 4, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 1, 0]]} "Class ", 2092, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 1, 4, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 1, 0]]} "Class ", 2093, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 1, 2, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 1, 4, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 1, 2, 3], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 0, 1]]} "Class ", 2094, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 1, 2, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 1, 4, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 1, 2, 3], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 0, 1]]} "Class ", 2095, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 1, 4, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 1, 1]]} "Class ", 2096, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 1, 1]]} "Class ", 2097, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 5, 3, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 5, 3, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 818, 3783, 18988, 102538, 591680, 3628282, 23535383, 160850076, 1154262552, 8670935082, 68007480908, 555593843855, 4717986962019, 41565676573313] "" "Class ", 2098, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 2, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 5, 3, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 2, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 5, 3, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [4, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 807, 3699, 18413, 98697, 565755, 3448765, 22251459, 151338939, 1081221617, 8089486089, 63212068155, 514653435577, 4356516014931, 38268460801779] "" "Class ", 2099, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 5, 3, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 4, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 0, 0]]} "Class ", 2100, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 2, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 5, 3, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 4, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 3, 5, 2, 1], [1, 1, 0, 0]]} "Class ", 2101, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 2, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 2, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 2, 1, 4], {3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 1, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 766, 3307, 15195, 73952, 379796, 2051680, 11625236, 68916776, 426461626, 2748885777, 18421457241, 128121193200, 923314316602, 6884424953476] "" "Class ", 2102, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 2, 1, 4], {3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 1, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 753, 3201, 14457, 69129, 348873, 1852761, 10325817, 60239769, 367019193, 2330342361, 15389820537, 105525739929, 750042514233, 5517779587161] "" "Class ", 2103, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 4, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 1, 0]]} "Class ", 2104, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 2, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 4, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 3, 5, 2, 1], [1, 1, 1, 0]]} "Class ", 2105, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 5, 3, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 5, 3, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {2}, {}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 766, 3330, 15576, 78147, 418895, 2389085, 14439567, 92142565, 618699540, 4357997180, 32113858795, 246961681838, 1977599889411, 16457069221945] "" "Class ", 2106, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 2, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 5, 3, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 2, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 5, 3, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 752, 3207, 14674, 71961, 377020, 2102152, 12426139, 77591180, 510076134, 3519500782, 25419316170, 191697384361, 1506167792649, 12304427160920] "" "Class ", 2107, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 5, 3, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 4, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 0, 1]]} "Class ", 2108, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 2, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 5, 3, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 4, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 3, 5, 2, 1], [1, 1, 0, 1]]} "Class ", 2109, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 2, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 2, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 2, 1, 4], {3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [4, 2, 5, 1, 3], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 1, 2], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 5, 2, 1], {4}, {[0, 0, 0, 0, 0, 1]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 187, 722, 2894, 11933, 50302, 215818, 939401, 4138240, 18414685, 82652140, 373741395, 1700978595, 7785649565, 35815838930, 165501331715] "" "Class ", 2110, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 2, 1, 4], {3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [4, 2, 5, 1, 3], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 3, 5, 1, 2], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 186, 705, 2730, 10701, 42246, 167505, 665970, 2652501, 10577406, 42214905, 168581610, 673504701, 2691578166, 10759039905, 43014439650] "" "Class ", 2111, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 4, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 1, 1]]} "Class ", 2112, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 3, 5, 2, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 3, 1, 4, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 3, 5, 2, 1], [1, 1, 1, 1]]} "Class ", 2113, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 2, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 5, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 4, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 2, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 5, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 4, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [4, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {}, {}], [[4, 3, 2, 1, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[5, 3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 4, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 817, 3764, 18799, 100991, 579732, 3536817, 22826470, 155235259, 1108618252, 8289208377, 64719621829, 526418222124, 4451284095903, 39055099516182] "" "Class ", 2114, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 2, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 4, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 2, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 4, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [4, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 777, 3395, 15835, 78271, 408051, 2234667, 12803435, 76524755, 475820211, 3070157531, 20515518747, 141700045675, 1009905638875, 7415991261371] "" "Class ", 2115, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 2, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 5, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 4, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 5, 4, 2, 1], [0, 1, 0, 0]]} "Class ", 2116, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 2, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 5, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 4, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 5, 4, 2, 1], [1, 1, 0, 0]]} "Class ", 2117, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 2, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 4, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 2, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 4, 5], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 2, 1, 4], {3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 1, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {}, {}], [[4, 3, 2, 1, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[5, 3, 2, 1, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 4, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 4, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 779, 3419, 16035, 79873, 420589, 2332005, 13569761, 82630211, 525215943, 3476975059, 23925650863, 170821688001, 1263367320941, 9664415504789] "" "Class ", 2118, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 2, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 2, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 2, 1, 4], {3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 1, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {1}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 748, 3117, 13562, 61239, 285849, 1374624, 6795542, 34460659, 179004438, 951045563, 5162714096, 28603669256, 161609628068, 930354317464] "" "Class ", 2119, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 2, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 4, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 5, 4, 2, 1], [0, 1, 1, 0]]} "Class ", 2120, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 2, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 4, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 5, 4, 2, 1], [1, 1, 1, 0]]} "Class ", 2121, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 2, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 5, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 4, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 2, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 5, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 4, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {}, {}], [[4, 3, 2, 1, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[5, 3, 2, 1, 4], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 4, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 764, 3297, 15229, 75113, 394416, 2197303, 12941403, 80311708, 523563729, 3575802971, 25522527103, 189954399138, 1471183537476, 11835079593479] "" "Class ", 2122, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 2, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 4, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 2, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 4, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {2}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 187, 719, 2859, 11683, 48967, 210563, 928571, 4200363, 19470171, 92449243, 449131499, 2231178123, 11321523547, 58644619339, 309803217899] "" "Class ", 2123, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 2, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 5, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 4, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 5, 4, 2, 1], [0, 1, 0, 1]]} "Class ", 2124, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 2, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 5, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 4, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 5, 4, 2, 1], [1, 1, 0, 1]]} "Class ", 2125, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 2, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 4, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[3, 5, 4, 2, 1], [0, 0, 1, 1]]} "Class ", 2126, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 2, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 2, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 2, 1, 4], {3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {2}, {[0, 0, 1, 0, 0]}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [4, 2, 5, 1, 3], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 3, 5, 1, 2], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 186, 709, 2791, 11285, 46831, 199457, 872003, 3912285, 18001059, 84879321, 409744699, 2023351789, 10210567007, 52615132657, 276611850131] "" "Class ", 2127, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 2, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 4, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 5, 4, 2, 1], [0, 1, 1, 1]]} "Class ", 2128, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 5, 4, 2, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[3, 1, 2, 4, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 5, 4, 2, 1], [1, 1, 1, 1]]} "Class ", 2129, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 2, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 4, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 2, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 4, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 820, 3807, 19188, 104061, 603111, 3714632, 24198196, 166055154, 1196259909, 9019837065, 70994579616, 581953959422, 4957714330624, 43811511493509] "" "Class ", 2130, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 4, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 4, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [4, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 807, 3699, 18413, 98697, 565755, 3448765, 22251459, 151338939, 1081221617, 8089486089, 63212068155, 514653435577, 4356516014931, 38268460801779] "" "Class ", 2131, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 2, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 4, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 3, 4, 2, 1], [0, 1, 0, 0]]} "Class ", 2132, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 2, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 4, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 3, 4, 2, 1], [1, 1, 0, 0]]} "Class ", 2133, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 2, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 4, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 2, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 4, 5], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 2, 1, 4], {3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 1, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 784, 3496, 16804, 86515, 474688, 2763325, 17000103, 110146144, 749316095, 5337762437, 39718304667, 308036155572, 2484985926825, 20814519187030] "" "Class ", 2134, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 2, 1, 4], {3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 1, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 768, 3339, 15513, 76595, 400101, 2202662, 12738060, 77157419, 488265591, 3220652515, 22097719935, 157419768122, 1162372379484, 8882502810923] "" "Class ", 2135, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 2, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 4, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 3, 4, 2, 1], [0, 1, 1, 0]]} "Class ", 2136, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 2, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 4, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 3, 4, 2, 1], [1, 1, 1, 0]]} "Class ", 2137, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 4, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 4, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {2}, {}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 769, 3383, 16153, 83290, 460823, 2719071, 17019679, 112507237, 782448245, 5706299996, 43514699388, 346102719798, 2864761830484, 24627221752796] "" "Class ", 2138, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 4, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 4, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 752, 3207, 14674, 71961, 377020, 2102152, 12426139, 77591180, 510076134, 3519500782, 25419316170, 191697384361, 1506167792649, 12304427160920] "" "Class ", 2139, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 2, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 4, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 3, 4, 2, 1], [0, 1, 0, 1]]} "Class ", 2140, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 2, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 4, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 3, 4, 2, 1], [1, 1, 0, 1]]} "Class ", 2141, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 2, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 4, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 2, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 4, 5], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 2, 1, 4], {3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [4, 2, 5, 1, 3], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 1, 2], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 5, 2, 1], {4}, {[0, 0, 0, 0, 0, 1]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 744, 3166, 14509, 71504, 377610, 2127574, 12733203, 80610181, 537758272, 3767512874, 27637087900, 211714981914, 1689713591745, 14020565659897] "" "Class ", 2142, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 2, 1, 4], {3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [4, 2, 5, 1, 3], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 3, 5, 1, 2], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 187, 724, 2936, 12433, 54897, 252403, 1206557, 5986700, 30782652, 163776253, 900390055, 5108613871, 29878739023, 179941706256, 1114712617660] "" "Class ", 2143, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 2, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 4, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 3, 4, 2, 1], [0, 1, 1, 1]]} "Class ", 2144, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 3, 2, 4, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]} "Class ", 2145, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 5, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 5, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [4, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {}, {}], [[4, 3, 2, 1, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[5, 3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 4, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 830, 3877, 19648, 107093, 623504, 3855942, 25212271, 173605326, 1254590130, 9487201320, 74875056148, 615308271379, 5254192065751, 46533794588620] "" "Class ", 2146, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [4, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 777, 3395, 15835, 78271, 408051, 2234667, 12803435, 76524755, 475820211, 3070157531, 20515518747, 141700045675, 1009905638875, 7415991261371] "" "Class ", 2147, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 5, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]} "Class ", 2148, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 2, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 5, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 5, 3, 2, 1], [1, 1, 0, 0]]} "Class ", 2149, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 5, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 5, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4, 5], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 2, 1, 4], {3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 1, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {}, {}], [[4, 3, 2, 1, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[5, 3, 2, 1, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [5, 4, 2, 1, 3], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 4, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 770, 3375, 15907, 80151, 429681, 2441032, 14644184, 92478003, 612993593, 4254160991, 30840132027, 233053305932, 1832322323684, 14962246242069] "" "Class ", 2150, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 2, 1, 4], {3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 1, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {3}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 186, 709, 2796, 11357, 47409, 203031, 890679, 3997139, 18328027, 85770813, 409246880, 1989108473, 9840110036, 49508823299, 253166957524] "" "Class ", 2151, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 5, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 1, 0]]} "Class ", 2152, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 2, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 5, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 5, 3, 2, 1], [1, 1, 1, 0]]} "Class ", 2153, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {}, {}], [[4, 3, 2, 1, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[5, 3, 2, 1, 4], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [5, 4, 2, 1, 3], {1, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 4, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 782, 3495, 16997, 89407, 505063, 3043645, 19456698, 131325649, 932268459, 6937370193, 53957822455, 437539791433, 3690702879674, 32319083424147] "" "Class ", 2154, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {2}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 187, 719, 2859, 11683, 48967, 210563, 928571, 4200363, 19470171, 92449243, 449131499, 2231178123, 11321523547, 58644619339, 309803217899] "" "Class ", 2155, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {3}, {[1, 0, 0, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {4}, {}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {4}, {}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {4}, {}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {4}, {}], [[3, 5, 2, 4, 1], {2, 3}, {}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {4}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3, 4}, {[1, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 187, 727, 2987, 12989, 59693, 289463, 1477913, 7926575, 44554313, 261870383, 1606044473, 10257666335, 68103177593, 469225436063, 3349761917753] "" "Class ", 2156, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 2, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 5, 3, 2, 1], [1, 1, 0, 1]]} "Class ", 2157, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 2, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[4, 5, 3, 2, 1], [0, 0, 1, 1]]} "Class ", 2158, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 2, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 2, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 2, 1, 4], {3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {3}, {[0, 1, 0, 0, 0]}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [4, 2, 5, 1, 3], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 3, 5, 1, 2], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 5, 2, 1], {4}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 183, 658, 2296, 7610, 23611, 68033, 181745, 451407, 1047975, 2288466, 4730458, 9311122, 17545163, 31798885, 55660691] "" "Class ", 2159, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]} "Class ", 2160, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[4, 5, 3, 2, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[4, 5, 3, 2, 1], [1, 1, 1, 1]]} "Class ", 2161, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [4, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {}, {}], [[4, 3, 2, 1, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[5, 3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [5, 4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 800, 3630, 17737, 92778, 515870, 3032683, 18777016, 121981360, 828601616, 5870241171, 43267948115, 331050757449, 2624254647778, 21515971593660] "" "Class ", 2162, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [4, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 754, 3253, 14988, 73390, 379064, 2058487, 11709194, 69491888, 429336566, 2754108193, 18300611708, 125750482306, 891894248860, 6519151756411] "" "Class ", 2163, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]} "Class ", 2164, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]} "Class ", 2165, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 2, 1, 4], {3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 1, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {}, {}], [[4, 3, 2, 1, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[5, 3, 2, 1, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [5, 4, 2, 1, 3], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [5, 4, 3, 1, 2], {1, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 187, 732, 3032, 13213, 60356, 287976, 1430805, 7385746, 39524479, 218796442, 1251105280, 7376251258, 44782792278, 279583069411, 1792881039119] "" "Class ", 2166, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 2, 1, 4], {3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 1, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 183, 680, 2598, 10183, 40921, 168408, 709190, 3053346, 13426470, 60250750, 275675504, 1285071833, 6098564463, 29443983200, 144528614138] "" "Class ", 2167, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 1, 0]]} "Class ", 2168, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]} "Class ", 2169, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {}, {}], [[4, 3, 2, 1, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[5, 3, 2, 1, 4], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [5, 4, 2, 1, 3], {1, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [5, 4, 3, 1, 2], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 747, 3171, 14340, 68893, 350100, 1871901, 10493463, 61417008, 374340164, 2370141732, 15547364949, 105496801156, 739035758588, 5335927128447] "" "Class ", 2170, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 184, 691, 2661, 10482, 42387, 176353, 755306, 3324902, 15036479, 69750565, 331613182, 1613773146, 8031832617, 40840270739, 211995685120] "" "Class ", 2171, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 1, 4], {}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 1, 3], {}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {3}, {[1, 0, 0, 0, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {4}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[2, 5, 4, 3, 1], {1, 4}, {[1, 0, 0, 0, 0, 0]}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2}, {}], [[4, 2, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {1, 2}, {}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {4}, {}], [[4, 3, 2, 5, 1], {3, 4}, {}], [[5, 2, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2}, {}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {4}, {}], [[5, 3, 2, 4, 1], {3, 4}, {}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {4}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {3, 4}, {[1, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 183, 671, 2476, 9195, 34333, 129529, 495244, 1921310, 7571210, 30312427, 123329635, 509840963, 2141399162, 9134776074, 39570327407] "" "Class ", 2172, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]} "Class ", 2173, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]} "Class ", 2174, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 2, 1, 4], {3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {3}, {[1, 0, 0, 0, 0]}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [4, 2, 5, 1, 3], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 3, 5, 1, 2], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 5, 2, 1], {4}, {[0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 180, 626, 2069, 6340, 17634, 44012, 98842, 202784, 386474, 693152, 1181734, 1930220, 3039438, 4637124, 6882338] "" "Class ", 2175, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]} "Class ", 2176, " is:" {{[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 0]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 0]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]} "Class ", 2177, " is:" {{[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1265, 4147, 13798, 46476, 158170, 543050, 1878670, 6542330, 22915999, 80682987, 285378270, 1013564805, 3613262795] "" "Class ", 2178, " is:" {{[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 5, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 5, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1210, 3865, 12482, 40677, 133572, 441468, 1467296, 4900760, 16439370, 55357305, 187050302, 633998079, 2154950454] "" "Class ", 2179, " is:" {{[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 5, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[5, 1, 2, 3, 4], [0, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1, 5], [0, 1, 0, 0]]} "Class ", 2180, " is:" {{[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 5, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[5, 1, 2, 3, 4], [0, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 5, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[5, 1, 2, 3, 4], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 2, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 2181, " is:" {{[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 5, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[5, 1, 2, 3, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1, 5], [0, 0, 1, 0]]} "Class ", 2182, " is:" {{[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 5, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[5, 1, 2, 3, 4], [0, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 5, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[5, 1, 2, 3, 4], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1156, 3591, 11216, 35171, 110616, 348683, 1101039, 3481545, 11020920, 34917921, 110711507, 351233255, 1114841594] "" "Class ", 2183, " is:" {{[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 5, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[5, 1, 2, 3, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1, 5], [0, 1, 1, 0]]} "Class ", 2184, " is:" {{[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 5, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[5, 1, 2, 3, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 1, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 5, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[5, 1, 2, 3, 4], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 2, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 2, 0, 0]}] , [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 2185, " is:" {{[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1265, 4147, 13798, 46476, 158170, 543050, 1878670, 6542330, 22915999, 80682987, 285378270, 1013564805, 3613262795] "" "Class ", 2186, " is:" {{[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 5, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 5, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1210, 3865, 12482, 40677, 133572, 441468, 1467296, 4900760, 16439370, 55357305, 187050302, 633998079, 2154950454] "" "Class ", 2187, " is:" {{[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 5, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1, 5], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 5, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1, 5], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 2, 1, 4], {1}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [4, 2, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 3, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 383, 1202, 3819, 12253, 39624, 128963, 421957, 1386682, 4573831, 15133117, 50201885, 166913200, 556039112, 1855462213] "" "Class ", 2188, " is:" {{[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 5, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 5, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 2, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 2189, " is:" {{[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 5, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 5, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1]}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [4, 2, 1, 5, 3], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 3, 1, 5, 2], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 2, 5, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1220, 3926, 12785, 42031, 139257, 464397, 1557255, 5246765, 17750713, 60271723, 205307562, 701357930, 2402101862] "" "Class ", 2190, " is:" {{[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 5, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 5, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1156, 3591, 11216, 35171, 110616, 348683, 1101039, 3481545, 11020920, 34917921, 110711507, 351233255, 1114841594] "" "Class ", 2191, " is:" {{[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 5, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1, 5], [0, 1, 1, 1]]} "Class ", 2192, " is:" {{[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 5, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 5, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 2, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 2, 0, 0]}] , [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 2193, " is:" {{[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 1, 5, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 5, 1, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 5, 1, 2, 3], [0, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 1, 5, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 5, 1, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 5, 1, 2, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 5, 4, 2], {1, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 2, 5, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1265, 4147, 13803, 46529, 158536, 545143, 1889450, 6594230, 23154448, 81741938, 289962718, 1033025608, 3694603600] "" "Class ", 2194, " is:" {{[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 1, 5, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 5, 1, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 1, 5, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 5, 1, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 1, 4, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1210, 3867, 12504, 40833, 134482, 446197, 1490068, 5004702, 16895480, 57299652, 195130472, 666990671, 2287644406] "" "Class ", 2195, " is:" {{[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 1, 5, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 5, 1, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 5, 1, 2, 3], [0, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 1]], [[3, 2, 1, 5, 4], [0, 1, 0, 0]]} "Class ", 2196, " is:" {{[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 1, 5, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 5, 1, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 5, 1, 2, 3], [0, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 1, 5, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 5, 1, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 5, 1, 2, 3], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1], [0, 0, 2, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 2197, " is:" {{[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 1, 5, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 5, 1, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 1, 5, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 5, 1, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 5, 4, 2], {1, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 2, 5, 4, 1], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 392, 1255, 4081, 13438, 44696, 149897, 506188, 1719347, 5869205, 20121645, 69242786, 239063401, 827776060, 2873649884] "" "Class ", 2198, " is:" {{[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 1, 5, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 1, 5, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 1, 4, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 383, 1200, 3800, 12128, 38941, 125620, 406740, 1320880, 4299846, 14024774, 45818691, 149890564, 490902209, 1609263070] "" "Class ", 2199, " is:" {{[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 1, 5, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 5, 1, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 5, 1, 2, 3], [0, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 1]], [[3, 2, 1, 5, 4], [0, 1, 1, 0]]} "Class ", 2200, " is:" {{[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 1, 5, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 5, 1, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [0, 1, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 1, 5, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 5, 1, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1], [0, 0, 2, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 2201, " is:" {{[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 1, 5, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 5, 1, 2, 3], [1, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 1, 5, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 5, 1, 2, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {1, 3}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 5, 4, 2], {1, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 2, 5, 4, 1], {1, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1210, 3865, 12482, 40677, 133572, 441468, 1467296, 4900760, 16439370, 55357305, 187050302, 633998079, 2154950454] "" "Class ", 2202, " is:" {{[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 1, 5, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 5, 1, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 5, 1, 2, 3], [1, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 1, 5, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 5, 1, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 5, 1, 2, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {1, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {1, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 2203, " is:" {{[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 1, 5, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 5, 1, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 5, 1, 2, 3], [1, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 1]], [[3, 2, 1, 5, 4], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 1, 5, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 5, 1, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 5, 1, 2, 3], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 2, 1, 5, 4], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 2, 1, 4], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {1}, {}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 2, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 3, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 5, 2, 1], {2, 3}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1156, 3591, 11216, 35171, 110616, 348683, 1101039, 3481545, 11020920, 34917921, 110711507, 351233255, 1114841594] "" "Class ", 2204, " is:" {{[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 1, 5, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 5, 1, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 5, 1, 2, 3], [1, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [1, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 1, 5, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 5, 1, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 5, 1, 2, 3], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 3}, {[0, 0, 0, 1], [0, 0, 2, 0]}], [[3, 1, 2], {1, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 2205, " is:" {{[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 1, 5, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 5, 1, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 5, 1, 2, 3], [1, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [1, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 1, 5, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 5, 1, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 5, 1, 2, 3], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {1, 3}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 5, 4, 2], {1, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 2, 5, 4, 1], {1, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1210, 3865, 12482, 40677, 133572, 441468, 1467296, 4900760, 16439370, 55357305, 187050302, 633998079, 2154950454] "" "Class ", 2206, " is:" {{[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 1, 5, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 5, 1, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 5, 1, 2, 3], [1, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 1, 5, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 5, 1, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 5, 1, 2, 3], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {1, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {1, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 2207, " is:" {{[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 1, 5, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 5, 1, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 5, 1, 2, 3], [1, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 1]], [[3, 2, 1, 5, 4], [0, 1, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 1, 5, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 5, 1, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 5, 1, 2, 3], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 2, 1, 5, 4], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {[0, 0, 0, 2]}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 2, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1156, 3591, 11216, 35171, 110616, 348683, 1101039, 3481545, 11020920, 34917921, 110711507, 351233255, 1114841594] "" "Class ", 2208, " is:" {{[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 1, 5, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 5, 1, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 5, 1, 2, 3], [1, 1, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [1, 1, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 1, 5, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 5, 1, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 5, 1, 2, 3], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 1, 5, 4, 3], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 3}, {[0, 0, 0, 1], [0, 0, 2, 0]}], [[3, 1, 2], {1, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 2209, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 5, 1, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 5, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 5, 2, 3], [0, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 5, 1, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 5, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 5, 2, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1265, 4147, 13803, 46529, 158536, 545143, 1889450, 6594230, 23154448, 81741938, 289962718, 1033025608, 3694603600] "" "Class ", 2210, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 5, 1, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 5, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 5, 2, 3], [0, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 5, 1, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 5, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 5, 2, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, %1], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, %1], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, %1], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} %1 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 386, 1228, 3972, 13028, 43237, 144910, 489765, 1667436, 5713219, 19685682, 68168887, 237114968, 828081391, 2902426302] "" "Class ", 2211, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 5, 1, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 5, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 5, 2, 3], [0, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [0, 0, 1, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 5, 1, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 5, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 5, 2, 3], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [0, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1210, 3861, 12438, 40371, 131837, 432698, 1426111, 4717004, 15649744, 52059918, 173586012, 579997041, 1941515976] "" "Class ", 2212, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 5, 1, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 5, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 5, 2, 3], [0, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 5, 1, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 5, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 5, 2, 3], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 2, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 376, 1167, 3665, 11617, 37102, 119252, 385386, 1251307, 4079515, 13348068, 43814637, 144233139, 476027908, 1574765316] "" "Class ", 2213, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 5, 1, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 5, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 5, 2, 3], [0, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 5, 1, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 5, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 5, 2, 3], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 2214, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 5, 1, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 5, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 5, 2, 3], [0, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 5, 1, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 5, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 5, 2, 3], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 2215, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 5, 1, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 5, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 5, 2, 3], [0, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [0, 1, 1, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 5, 1, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 5, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 5, 2, 3], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 2216, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 5, 1, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 5, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 5, 2, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [0, 1, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 5, 1, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 5, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 5, 2, 3], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 2, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 2217, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 5, 1, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 5, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 5, 2, 3], [1, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 5, 1, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 5, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 5, 2, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1213, 3893, 12658, 41601, 137968, 461131, 1551671, 5252218, 17871292, 61092824, 209718021, 722626830, 2498458052] "" "Class ", 2218, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 5, 1, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 5, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 5, 2, 3], [1, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 5, 1, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 5, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 5, 2, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 376, 1167, 3665, 11617, 37102, 119252, 385386, 1251307, 4079515, 13348068, 43814637, 144233139, 476027908, 1574765316] "" "Class ", 2219, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 5, 1, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 5, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 5, 2, 3], [1, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [1, 0, 1, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 5, 1, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 5, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 5, 2, 3], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 2220, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 5, 1, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 5, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 5, 2, 3], [1, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [1, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 5, 1, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 5, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 5, 2, 3], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 2, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 2221, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 5, 1, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 5, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 5, 2, 3], [1, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [1, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 5, 1, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 5, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 5, 2, 3], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 2222, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 5, 1, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 5, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 5, 2, 3], [1, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 5, 1, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 5, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 5, 2, 3], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 2223, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 5, 1, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 5, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 5, 2, 3], [1, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [1, 1, 1, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 5, 1, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 5, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 5, 2, 3], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 2224, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 5, 2, 1, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 5, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 5, 3], [0, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 5, 2, 1, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 5, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 5, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}] , [[3, 5, 4, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1268, 4172, 13948, 47243, 161794, 559305, 1949100, 6839926, 24150658, 85734539, 305825890, 1095634003, 3940433424] "" "Class ", 2225, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 5, 2, 1, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 5, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 5, 3], [0, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 5, 2, 1, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 5, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 5, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [ [2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1213, 3895, 12680, 41757, 138858, 465618, 1572591, 5344816, 18266550, 62736189, 216417159, 749523870, 2605164990] "" "Class ", 2226, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 5, 2, 1, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 5, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 5, 3], [0, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [0, 0, 1, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 5, 2, 1, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 5, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 5, 3], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [0, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 4, 2, 1], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 2227, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 5, 2, 1, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 5, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 5, 3], [0, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 5, 2, 1, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 5, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 5, 3], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [ [2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 2228, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 5, 2, 1, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 5, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 5, 3], [0, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 1]], [[3, 5, 2, 1, 4], [0, 0, 1, 0]]} "Class ", 2229, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 5, 2, 1, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 5, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 5, 3], [0, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 5, 2, 1, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 5, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 5, 3], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, %1], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, %1], [[3, 4, 1, 2], {1, 2}, %1], [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [3, 5, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} %1 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 364, 1083, 3208, 9462, 27812, 81545, 238696, 698005, 2040025, 5960779, 17415475, 50882771, 148670706, 434413073] "" "Class ", 2230, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 5, 2, 1, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 5, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 5, 3], [0, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 1]], [[3, 5, 2, 1, 4], [0, 1, 1, 0]]} "Class ", 2231, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 5, 2, 1, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 5, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 5, 3], [0, 1, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [0, 1, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 5, 2, 1, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 5, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 5, 3], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, %1], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, %1], [[3, 4, 1, 2], {1, 2}, %1], [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [3, 5, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} %1 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 364, 1083, 3208, 9462, 27812, 81545, 238696, 698005, 2040025, 5960779, 17415475, 50882771, 148670706, 434413073] "" "Class ", 2232, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 5, 2, 1, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 5, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 5, 3], [1, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 5, 2, 1, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 5, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 5, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1213, 3893, 12658, 41601, 137968, 461131, 1551671, 5252218, 17871292, 61092824, 209718021, 722626830, 2498458052] "" "Class ", 2233, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 5, 2, 1, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 5, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 5, 3], [1, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 5, 2, 1, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 5, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 5, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [ [2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 2234, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 5, 2, 1, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 5, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 5, 3], [1, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [1, 0, 1, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 5, 2, 1, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 5, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 5, 3], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 4, 2, 1], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 2235, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 5, 2, 1, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 5, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 5, 3], [1, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [1, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 5, 2, 1, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 5, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 5, 3], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [ [2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 2236, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 5, 2, 1, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 5, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 5, 3], [1, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 1]], [[3, 5, 2, 1, 4], [0, 0, 1, 1]]} "Class ", 2237, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 5, 2, 1, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 5, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 5, 3], [1, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 5, 2, 1, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 5, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 5, 3], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, %1], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, %1], [[3, 4, 1, 2], {1, 2}, %1], [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [3, 5, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} %1 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 364, 1083, 3208, 9462, 27812, 81545, 238696, 698005, 2040025, 5960779, 17415475, 50882771, 148670706, 434413073] "" "Class ", 2238, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 5, 2, 1, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 5, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 5, 3], [1, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 1]], [[3, 5, 2, 1, 4], [0, 1, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 5, 2, 1, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 5, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 5, 3], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 5, 2, 1, 4], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [3, 5, 1, 4, 2], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 364, 1083, 3208, 9462, 27812, 81545, 238696, 698005, 2040025, 5960779, 17415475, 50882771, 148670706, 434413073] "" "Class ", 2239, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 5, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [0, 0, 0, 0]]} {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 5, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {}, {}], [[4, 3, 2, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[5, 3, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [5, 4, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1265, 4151, 13838, 46740, 159626, 550308, 1912604, 6694220, 23575055, 83477723, 297024532, 1061444895, 3808012875] "" "Class ", 2240, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 5, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 5, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1210, 3865, 12482, 40677, 133572, 441468, 1467296, 4900760, 16439370, 55357305, 187050302, 633998079, 2154950454] "" "Class ", 2241, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 5, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [0, 1, 0, 0]]} "Class ", 2242, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 5, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 5, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3, 5], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 1, 0, 0]}], [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3}, { [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 4, 2, 1], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 1, 0, 0], [0, 1, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 2243, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 5, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [0, 0, 1, 0]]} "Class ", 2244, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 5, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [1, 0, 1, 0]]} "Class ", 2245, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 5, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [0, 1, 1, 0]]} "Class ", 2246, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 5, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [1, 1, 1, 0]]} "Class ", 2247, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {1}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 376, 1167, 3669, 11664, 37438, 121170, 395038, 1296172, 4277073, 14184740, 47256112, 158074199, 530716070, 1787788655] "" "Class ", 2248, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {1}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 376, 1167, 3669, 11664, 37438, 121170, 395038, 1296172, 4277073, 14184740, 47256112, 158074199, 530716070, 1787788655] "" "Class ", 2249, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 5, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 5, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 2, 1, 4], {2}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {2, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {1}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [4, 2, 5, 1, 3], {1, 2, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 3, 5, 1, 2], {1, 2, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 356, 1043, 3047, 8889, 25923, 75623, 220759, 645000, 1886305, 5521822, 16179451, 47450509, 139281925, 409171207] "" "Class ", 2250, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 5, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 5, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3, 5], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 2, 1, 4], {2}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {2, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {1}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [4, 2, 5, 1, 3], {1, 2, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 3, 5, 1, 2], {1, 2, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 356, 1043, 3047, 8889, 25923, 75623, 220759, 645000, 1886305, 5521822, 16179451, 47450509, 139281925, 409171207] "" "Class ", 2251, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 5, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 5, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3, 5], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {1}, {[0, 0, 0, 1, 0]}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 2, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {4}, %1], [[4, 3, 1, 5, 2], {1, 2, 4}, { [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 2, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0]}], [[5, 2, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {4}, %1], [[5, 3, 1, 4, 2], {1, 2, 4}, { [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 3, 2, 4, 1], {1, 2, 3}, %1]} %1 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 357, 1053, 3108, 9185, 27185, 80584, 239227, 711159, 2116732, 6307481, 18814332, 56172130, 167846923, 501916963] "" "Class ", 2252, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 5, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [1, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 5, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3, 5], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {1}, {[0, 0, 0, 1, 0]}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 2, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {4}, %1], [[4, 3, 1, 5, 2], {1, 2, 4}, { [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 2, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0]}], [[5, 2, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {4}, %1], [[5, 3, 1, 4, 2], {1, 2, 4}, { [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 3, 2, 4, 1], {1, 2, 3}, %1]} %1 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 357, 1053, 3108, 9185, 27185, 80584, 239227, 711159, 2116732, 6307481, 18814332, 56172130, 167846923, 501916963] "" "Class ", 2253, " is:" {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 5, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [0, 1, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 5, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3, 5], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 3, 2, 1, 4], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 2, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {1}, {[0, 0, 0, 1, 0]}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [4, 2, 1, 5, 3], {4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 2, 5, 1, 3], {3, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 3, 1, 5, 2], {1, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 2, 5, 1], {1}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0]}], [ [4, 3, 5, 1, 2], {1, 2, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 119, 336, 924, 2492, 6636, 17536, 46137, 121095, 317434, 831571, 2177734, 5702191, 14929519, 39087182, 102332996] "" "Class ", 2254, " is:" {{[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 1, 5, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 5, 1, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 5, 1, 2, 4], [0, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 1, 5, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 5, 1, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 5, 1, 2, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {1, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 1, 5, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 127, 409, 1355, 4587, 15798, 55170, 194885, 695085, 2499597, 9052948, 32991902, 120893223, 445151781, 1646275987, 6112180686] "" "Class ", 2255, " is:" {{[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 1, 5, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 5, 1, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 5, 1, 2, 4], [0, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 1, 5, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 5, 1, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 5, 1, 2, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}] , [[3, 1, 4, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1265, 4150, 13828, 46674, 159262, 548498, 1904179, 6656720, 23413351, 82796431, 294203641, 1049919648, 3761410985] "" "Class ", 2256, " is:" {{[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 1, 5, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 5, 1, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 5, 1, 2, 4], [0, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 1]], [[4, 2, 1, 5, 3], [0, 1, 0, 0]]} "Class ", 2257, " is:" {{[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 1, 5, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 5, 1, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 5, 1, 2, 4], [0, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 1, 5, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 5, 1, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 5, 1, 2, 4], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1], [0, 1, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1211, 3875, 12548, 41040, 135370, 449791, 1504057, 5057668, 17092030, 58018150, 197727023, 676290905, 2320721255] "" "Class ", 2258, " is:" {{[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 1, 5, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 5, 1, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 5, 1, 2, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 1]], [[4, 2, 1, 5, 3], [0, 0, 1, 0]]} "Class ", 2259, " is:" {{[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 1, 5, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 5, 1, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 5, 1, 2, 4], [0, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 1]], [[4, 2, 1, 5, 3], [1, 0, 1, 0]]} "Class ", 2260, " is:" {{[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 1, 5, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 5, 1, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 5, 1, 2, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 1]], [[4, 2, 1, 5, 3], [0, 1, 1, 0]]} "Class ", 2261, " is:" {{[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 1, 5, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 5, 1, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 5, 1, 2, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 1]], [[4, 2, 1, 5, 3], [1, 1, 1, 0]]} "Class ", 2262, " is:" {{[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 1, 5, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 5, 1, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 5, 1, 2, 4], [1, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 1]], [[4, 2, 1, 5, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 1, 5, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 5, 1, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 5, 1, 2, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 2, 1, 5, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[4, 2, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1265, 4148, 13808, 46542, 158534, 544869, 1887212, 6580775, 23083823, 81399079, 288380766, 1025982051, 3664054185] "" "Class ", 2263, " is:" {{[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 1, 5, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 5, 1, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 5, 1, 2, 4], [1, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 1]], [[4, 2, 1, 5, 3], [1, 0, 0, 1]]} "Class ", 2264, " is:" {{[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 1, 5, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 5, 1, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 5, 1, 2, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 1]], [[4, 2, 1, 5, 3], [0, 1, 0, 1]]} "Class ", 2265, " is:" {{[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 1, 5, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 5, 1, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 5, 1, 2, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 1]], [[4, 2, 1, 5, 3], [1, 1, 0, 1]]} "Class ", 2266, " is:" {{[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 1, 5, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 5, 1, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 5, 1, 2, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 1]], [[4, 2, 1, 5, 3], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 1, 5, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 5, 1, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 5, 1, 2, 4], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 2, 1, 5, 3], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {[0, 0, 1, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1221, 3939, 12886, 42648, 142544, 480459, 1631287, 5574073, 19153815, 66146259, 229452587, 799140681, 2793373937] "" "Class ", 2267, " is:" {{[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 1, 5, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 5, 1, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 5, 1, 2, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 1]], [[4, 2, 1, 5, 3], [1, 0, 1, 1]]} "Class ", 2268, " is:" {{[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 1, 5, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 5, 1, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 5, 1, 2, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 1]], [[4, 2, 1, 5, 3], [0, 1, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 1, 5, 4, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 1, 5, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 5, 1, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 5, 1, 2, 4], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 2, 1, 5, 3], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {[0, 0, 1, 1]}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 1, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 376, 1167, 3665, 11615, 37073, 119010, 383841, 1242867, 4037778, 13155242, 42966387, 140636553, 461207567, 1515065297] "" "Class ", 2269, " is:" {{[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 5, 2, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 5, 2, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {1, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [3, 1, 5, 4, 2], {1, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 2, 5, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1265, 4153, 13853, 46819, 159988, 551824, 1918637, 6717492, 23663019, 83805980, 298239312, 1065915887, 3824410116] "" "Class ", 2270, " is:" {{[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 5, 2, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 5, 2, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 376, 1167, 3670, 11679, 37564, 121983, 399544, 1318798, 4383174, 14658246, 49292423, 166586088, 565514229, 1927557260] "" "Class ", 2271, " is:" {{[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 5, 2, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [0, 1, 0, 0]]} "Class ", 2272, " is:" {{[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 5, 2, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [1, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 5, 2, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2, 5], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 2, 1, 4], {2}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {2}, {}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 2, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 3, 5, 1, 2], {1, 2, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[5, 2, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 3, 2, 4, 1], {2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 356, 1042, 3037, 8827, 25618, 74315, 215632, 626120, 1819845, 5295578, 15428589, 45006923, 131450682, 384376649] "" "Class ", 2273, " is:" {{[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 5, 2, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [0, 0, 1, 0]]} "Class ", 2274, " is:" {{[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 5, 2, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [1, 0, 1, 0]]} "Class ", 2275, " is:" {{[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 5, 2, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [0, 1, 1, 0]]} "Class ", 2276, " is:" {{[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 5, 2, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [1, 1, 1, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 5, 2, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2, 5], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 2, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {2}, {}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 2, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 2, 5, 1, 3], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 3, 1, 5, 2], {1, 4, 5}, %1], [[4, 3, 2, 5, 1], {2}, {[0, 0, 0, 0, 0, 1]}], [[4, 3, 5, 1, 2], {1, 2, 5}, %1], [[4, 3, 5, 2, 1], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[5, 2, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 4, 5}, %1], [[5, 3, 2, 4, 1], {2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} %1 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 120, 348, 1002, 2876, 8253, 23717, 68306, 197200, 570671, 1655112, 4810025, 14004288, 40840413, 119279153, 348837048] "" "Class ", 2277, " is:" {{[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 5, 2, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 5, 2, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {1, 3}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {1, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}] , [[3, 1, 5, 4, 2], {1, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 2, 5, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1213, 3895, 12680, 41757, 138858, 465618, 1572591, 5344816, 18266550, 62736189, 216417159, 749523870, 2605164990] "" "Class ", 2278, " is:" {{[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 5, 2, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 5, 2, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {1, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 2279, " is:" {{[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 5, 2, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [0, 1, 0, 1]]} "Class ", 2280, " is:" {{[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 5, 2, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 5, 2, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2, 5], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {3, 4}, %1], [[3, 2, 1, 4], {2}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 4}, %1], [[4, 3, 1, 2], {1, 4}, %1], [[4, 3, 2, 1], {2}, {}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [4, 2, 5, 1, 3], {1, 2, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 5, 1, 2], {1, 2, 5}, { [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2}, {[0, 0, 0, 0, 0, 1]}]} %1 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 120, 345, 972, 2691, 7348, 19855, 53230, 141871, 376466, 995705, 2627018, 6918101, 18192804, 47791365, 125443416] "" "Class ", 2281, " is:" {{[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 5, 2, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 5, 2, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2, 5], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {[0, 0, 2, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9843, 29537, 88663, 266242, 799804, 2403648, 7226699, 21736425, 65404822, 196878214, 592848347] "" "Class ", 2282, " is:" {{[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 5, 2, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [1, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 5, 2, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2, 5], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {2}, {[0, 0, 2, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 356, 1043, 3047, 8889, 25923, 75623, 220759, 645000, 1886305, 5521822, 16179451, 47450509, 139281925, 409171207] "" "Class ", 2283, " is:" {{[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 5, 2, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [0, 1, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 5, 2, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2, 5], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {[0, 0, 2, 0]}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 2, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 2, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 120, 346, 982, 2754, 7663, 21222, 58619, 161700, 445772, 1228595, 3385904, 9331302, 25717075, 70878304, 195350707] "" "Class ", 2284, " is:" {{[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 5, 2, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [1, 1, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 2, 5, 4, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 5, 2, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2, 5], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 2, 1, 4, 3], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {2}, {[0, 0, 2, 0]}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 2, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 119, 336, 924, 2492, 6636, 17536, 46137, 121095, 317434, 831571, 2177734, 5702191, 14929519, 39087182, 102332996] "" "Class ", 2285, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 5, 1, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 5, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 5, 2, 4], [0, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 5, 1, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 5, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 5, 2, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 127, 409, 1355, 4587, 15798, 55170, 194885, 695085, 2499597, 9052948, 32991902, 120893223, 445151781, 1646275987, 6112180686] "" "Class ", 2286, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 5, 1, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 5, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 5, 2, 4], [0, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 5, 1, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 5, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 5, 2, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 394, 1273, 4194, 14039, 47614, 163266, 565072, 1971476, 6926313, 24482914, 87009495, 310710172, 1114326403, 4011922558] "" "Class ", 2287, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 5, 1, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 5, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 5, 2, 4], [0, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 1]], [[4, 2, 5, 1, 3], [0, 1, 0, 0]]} "Class ", 2288, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 5, 1, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 5, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 5, 2, 4], [0, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 5, 1, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 5, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 5, 2, 4], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 1, 1, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1220, 3929, 12822, 42309, 140922, 473169, 1599864, 5442561, 18615176, 63975857, 220816906, 765121477, 2660426630] "" "Class ", 2289, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 5, 1, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 5, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 5, 2, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 1]], [[4, 2, 5, 1, 3], [0, 0, 1, 0]]} "Class ", 2290, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 5, 1, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 5, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 5, 2, 4], [0, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 5, 1, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 5, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 5, 2, 4], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}] , [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 2291, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 5, 1, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 5, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 5, 2, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 1]], [[4, 2, 5, 1, 3], [0, 1, 1, 0]]} "Class ", 2292, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 5, 1, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 5, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 5, 2, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [0, 1, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 5, 1, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 5, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 5, 2, 4], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1], [0, 1, 1, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}] , [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1], [0, 0, 1, 1, 0], [0, 1, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 2293, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 5, 1, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 5, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 5, 2, 4], [1, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 1]], [[4, 2, 5, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 5, 1, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 5, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 5, 2, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 2, 5, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4157, 13863, 46827, 159886, 550943, 1913526, 6691891, 23544320, 83280751, 295986327, 1056461081, 3785365874] "" "Class ", 2294, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 5, 1, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 5, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 5, 2, 4], [1, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 1]], [[4, 2, 5, 1, 3], [1, 0, 0, 1]]} "Class ", 2295, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 5, 1, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 5, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 5, 2, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 1]], [[4, 2, 5, 1, 3], [0, 1, 0, 1]]} "Class ", 2296, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 5, 1, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 5, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 5, 2, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 1]], [[4, 2, 5, 1, 3], [1, 1, 0, 1]]} "Class ", 2297, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 5, 1, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 5, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 5, 2, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 1]], [[4, 2, 5, 1, 3], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 5, 1, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 5, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 5, 2, 4], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 2, 5, 1, 3], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 376, 1168, 3680, 11740, 37865, 123302, 404908, 1339559, 4460835, 14941827, 50310068, 170191778, 578169963, 1971665691] "" "Class ", 2298, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 5, 1, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 5, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 5, 2, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 1]], [[4, 2, 5, 1, 3], [1, 0, 1, 1]]} "Class ", 2299, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 5, 1, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 5, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 5, 2, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 1]], [[4, 2, 5, 1, 3], [0, 1, 1, 1]]} "Class ", 2300, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 2, 5, 1, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 5, 3], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 5, 2, 4], [1, 1, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 1, 4, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 1]], [[4, 2, 5, 1, 3], [1, 1, 1, 1]]} "Class ", 2301, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 4, 1, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 5, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 4, 1, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 5, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [3, 5, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 395, 1281, 4238, 14250, 48548, 167215, 581338, 2037323, 7189654, 25527147, 91124468, 326850124, 1177406867, 4257789401] "" "Class ", 2302, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 4, 1, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 5, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 4, 1, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 5, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 378, 1188, 3802, 12352, 40652, 135269, 454324, 1538273, 5245113, 17995060, 62075102, 215173461, 749113540, 2618223790] "" "Class ", 2303, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 4, 1, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 5, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 2, 4, 1, 3], [0, 1, 0, 0]]} "Class ", 2304, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 4, 1, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 5, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 4, 1, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 5, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2, 5], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1], [0, 1, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 358, 1067, 3214, 9788, 30111, 93469, 292469, 921637, 2922470, 9318414, 29858927, 96100247, 310529452, 1007036638] "" "Class ", 2305, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 4, 1, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 5, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 4, 1, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 5, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2, 5], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [3, 5, 1, 4, 2], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 376, 1167, 3665, 11617, 37102, 119252, 385386, 1251307, 4079515, 13348068, 43814637, 144233139, 476027908, 1574765316] "" "Class ", 2306, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 4, 1, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 5, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 4, 1, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 5, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2, 5], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 354, 1021, 2901, 8130, 22513, 61713, 167746, 452789, 1215197, 3246050, 8637641, 22912633, 60624546, 160075117] "" "Class ", 2307, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 4, 1, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 5, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 2, 4, 1, 3], [0, 1, 1, 0]]} "Class ", 2308, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 4, 1, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 5, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [0, 1, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 4, 1, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 5, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2, 5], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1], [0, 1, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 120, 345, 972, 2691, 7348, 19855, 53230, 141871, 376466, 995705, 2627018, 6918101, 18192804, 47791365, 125443416] "" "Class ", 2309, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 4, 1, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 5, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 4, 1, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 5, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [3, 5, 1, 4, 2], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 386, 1228, 3972, 13028, 43237, 144910, 489765, 1667436, 5713219, 19685682, 68168887, 237114968, 828081391, 2902426302] "" "Class ", 2310, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 4, 1, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 5, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 4, 1, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 5, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 367, 1117, 3438, 10683, 33461, 105530, 334859, 1068333, 3424956, 11027792, 35646926, 115637003, 376335371, 1228390033] "" "Class ", 2311, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 4, 1, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 5, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 2, 4, 1, 3], [0, 1, 0, 1]]} "Class ", 2312, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 4, 1, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 5, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [1, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 4, 1, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 5, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2, 5], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1], [0, 1, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 120, 345, 972, 2691, 7348, 19855, 53230, 141871, 376466, 995705, 2627018, 6918101, 18192804, 47791365, 125443416] "" "Class ", 2313, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 4, 1, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 5, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [1, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 4, 1, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 5, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2, 5], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [3, 5, 1, 4, 2], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 376, 1167, 3665, 11617, 37102, 119252, 385386, 1251307, 4079515, 13348068, 43814637, 144233139, 476027908, 1574765316] "" "Class ", 2314, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 4, 1, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 5, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 4, 1, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 5, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2, 5], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 354, 1021, 2901, 8130, 22513, 61713, 167746, 452789, 1215197, 3246050, 8637641, 22912633, 60624546, 160075117] "" "Class ", 2315, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 2, 4, 1, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 5, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 2, 4, 1, 3], [0, 1, 1, 1]]} "Class ", 2316, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 5, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 5, 4], [0, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 5, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 5, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 127, 409, 1356, 4592, 15818, 55244, 195155, 696060, 2503115, 9065672, 33038110, 121061765, 445769241, 1648547621, 6120571185] "" "Class ", 2317, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 5, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 5, 4], [0, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 5, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 5, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [ [2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1267, 4166, 13918, 47109, 161205, 556783, 1938487, 6796031, 23971361, 85009671, 302918609, 1084049439, 3894514424] "" "Class ", 2318, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 5, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 5, 4], [0, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 5, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 5, 4], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {4}, %1], [[3, 5, 2, 1, 4], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {4}, %1], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 5, 3, 1, 2], {3}, %1], [[4, 5, 3, 2, 1], {3}, {[0, 0, 0, 0, 0, 1]}]} %1 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1211, 3871, 12497, 40637, 132839, 435926, 1434667, 4731840, 15632350, 51709271, 171214175, 567343342, 1881122669] "" "Class ", 2319, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 5, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 5, 4], [0, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 5, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 5, 4], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 2320, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 5, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 5, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [0, 0, 1, 0]]} "Class ", 2321, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 5, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 5, 4], [0, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 5, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 5, 4], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {2, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}] , [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [3, 5, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2, 5}, { [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 364, 1084, 3219, 9535, 28191, 83244, 245611, 724323, 2135475, 6294893, 18554337, 54686932, 161180452, 475047349] "" "Class ", 2322, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 5, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 5, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 1, 1, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 5, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 5, 4], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 4, 1, 3], {2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [3, 5, 1, 4, 2], {5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 4, 1], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 4, 2, 1], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 2323, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 5, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 5, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 1, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 5, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 5, 4], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [3, 5, 1, 4, 2], {3, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 4, 1], {3, 5}, { [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 353, 1010, 2830, 7778, 21027, 56083, 148003, 387428, 1008152, 2612468, 6751445, 17420701, 44920853, 115834550] "" "Class ", 2324, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 5, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 5, 4], [1, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 5, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 5, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4157, 13863, 46827, 159886, 550943, 1913526, 6691891, 23544320, 83280751, 295986327, 1056461081, 3785365874] "" "Class ", 2325, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 5, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 5, 4], [1, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [1, 0, 0, 1]]} "Class ", 2326, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 5, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 5, 4], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 373, 1136, 3462, 10538, 32010, 96997, 293191, 884106, 2660077, 7987470, 23940983, 71644479, 214099942, 639030894] "" "Class ", 2327, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 5, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 5, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [1, 1, 0, 1]]} "Class ", 2328, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 5, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 5, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [0, 0, 1, 1]]} "Class ", 2329, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 5, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 5, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [1, 0, 1, 1]]} "Class ", 2330, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 5, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 5, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 5, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 5, 4], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 354, 1021, 2901, 8130, 22513, 61713, 167746, 452789, 1215197, 3246050, 8637641, 22912633, 60624546, 160075117] "" "Class ", 2331, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 5, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 4, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 5, 3], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 4, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [3, 5, 4, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1265, 4153, 13853, 46819, 159988, 551824, 1918637, 6717492, 23663019, 83805980, 298239312, 1065915887, 3824410116] "" "Class ", 2332, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 5, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 4, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 5, 3], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 4, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [ [2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 376, 1170, 3702, 11892, 38710, 127449, 423721, 1420544, 4797006, 16301500, 55705697, 191300243, 659854513, 2285099356] "" "Class ", 2333, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 5, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 4, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 5, 3], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 4, 5], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, %3], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1}, %4], [[2, 4, 3, 1], {1}, %4], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1}, %3], [[3, 2, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, %3], [[4, 2, 1, 3], {}, %4], [[4, 2, 3, 1], {3}, %4], [[4, 3, 1, 2], {}, %3], [[4, 3, 2, 1], {}, {}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 2, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {1, 2}, %2], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {1, 2}, %1], [[4, 3, 2, 1, 5], {3}, {[0, 0, 0, 0, 0, 1]}], [[4, 3, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[5, 2, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2}, %2], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2}, %1], [[5, 3, 2, 1, 4], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 3, 2, 4, 1], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2}, %1], [[5, 4, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 3}, %2], [[5, 4, 3, 1, 2], {1}, %1], [[5, 4, 3, 2, 1], {3}, {}]} %1 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]} %2 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]} %3 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]} %4 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 368, 1118, 3415, 10470, 32189, 99168, 306008, 945450, 2923988, 9050182, 28029591, 86856286, 269258158, 834998828] "" "Class ", 2334, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 5, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 4, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 5, 3], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 4, 5], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [ [2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 2, 0, 0, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 359, 1068, 3183, 9498, 28367, 84778, 253499, 758309, 2269129, 6791876, 20333793, 60887745, 182352663, 546204522] "" "Class ", 2335, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 5, 3], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 4, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [0, 0, 1, 0]]} "Class ", 2336, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 5, 3], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 4, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [1, 0, 1, 0]]} "Class ", 2337, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 5, 3], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 4, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [0, 1, 1, 0]]} "Class ", 2338, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 5, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 4, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 1, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 5, 3], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 4, 5], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 2, 0, 0, 0]}], [ [2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 2, 0, 0, 0], [1, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 2, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, { [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [ [3, 5, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 2, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 2, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 118, 327, 872, 2249, 5642, 13835, 33292, 78861, 184334, 425999, 974864, 2211857, 4980754, 11141139, 24772628] "" "Class ", 2339, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 4, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 4, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 2, 1, 4], {1, 2}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {1}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 367, 1113, 3405, 10506, 32669, 102318, 322527, 1022535, 3258606, 10432701, 33540845, 108241054, 350510458, 1138597841] "" "Class ", 2340, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 4, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 4, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, %1], [[2, 4, 3, 1], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {1, 2}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, %1], [[4, 2, 1, 3], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1}, %1], [[4, 3, 2, 1], {2}, {[0, 0, 1, 0, 0]}]} %1 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 120, 348, 1000, 2855, 8118, 23032, 65284, 185031, 524670, 1488972, 4230012, 12031191, 34262466, 97697865, 278939322] "" "Class ", 2341, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 4, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 4, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, %3], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1}, %4], [[2, 4, 3, 1], {1}, %4], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1}, %3], [[3, 2, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, %3], [[4, 2, 1, 3], {}, %4], [[4, 2, 3, 1], {3}, %4], [[4, 3, 1, 2], {}, %3], [[4, 3, 2, 1], {1}, {[0, 0, 1, 0, 0]}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 2, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {1, 2}, %1], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {1, 2}, %2], [[4, 3, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[5, 2, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2}, %1], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2}, %2], [[5, 3, 2, 4, 1], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2}, %2], [[5, 4, 2, 3, 1], {1, 3}, %1]} %1 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]} %2 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]} %3 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]} %4 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 120, 348, 997, 2830, 7980, 22412, 62816, 175956, 493081, 1383260, 3886366, 10938170, 30843294, 87138604, 246654918] "" "Class ", 2342, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 4, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 4, 5], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, %1], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1}, %2], [[2, 4, 3, 1], {1}, %2], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1}, %1], [[3, 2, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, %1], [[4, 2, 1, 3], {2}, %2], [[4, 2, 3, 1], {2}, %2], [[4, 3, 1, 2], {1}, %1], [[4, 3, 2, 1], {2}, {[0, 0, 1, 0, 0]}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [4, 2, 1, 5, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 2, 5, 1, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 3, 1, 5, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 2, 5, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [[4, 3, 5, 1, 2], {1, 2}, { [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0]}]} %1 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]} %2 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 119, 340, 959, 2684, 7483, 20838, 58054, 161963, 452720, 1268183, 3560513, 10018946, 28254539, 79850354, 226124441] "" "Class ", 2343, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 5, 3], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 4, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [0, 0, 1, 1]]} "Class ", 2344, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 5, 3], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 4, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [1, 0, 1, 1]]} "Class ", 2345, " is:" {{[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 5, 3], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[3, 1, 2, 4, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 4, 2, 1, 3], [0, 1, 1, 1]]} "Class ", 2346, " is:" {{[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 5, 1, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 5, 1, 3, 4], [0, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 5, 1, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 5, 1, 3, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 5, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 128, 415, 1382, 4697, 16226, 56797, 201002, 717970, 2585066, 9372151, 34185178, 125360624, 461906052, 1709227519, 6349161702] "" "Class ", 2347, " is:" {{[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 5, 1, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 5, 1, 3, 4], [0, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 5, 1, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 5, 1, 3, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 127, 409, 1355, 4588, 15803, 55190, 194960, 695359, 2500587, 9056520, 33004821, 120940129, 445322830, 1646902490, 6114485110] "" "Class ", 2348, " is:" {{[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 5, 1, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 5, 1, 3, 4], [0, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [0, 1, 0, 0]]} "Class ", 2349, " is:" {{[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 5, 1, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 5, 1, 3, 4], [0, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 5, 1, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 5, 1, 3, 4], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1], [0, 2, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1265, 4149, 13818, 46608, 158898, 546685, 1895715, 6618905, 23249607, 82103555, 291322471, 1038099516, 3713430835] "" "Class ", 2350, " is:" {{[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 5, 1, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 5, 1, 3, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [0, 0, 1, 0]]} "Class ", 2351, " is:" {{[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 5, 1, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 5, 1, 3, 4], [0, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [1, 0, 1, 0]]} "Class ", 2352, " is:" {{[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 5, 1, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 5, 1, 3, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [0, 1, 1, 0]]} "Class ", 2353, " is:" {{[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 5, 1, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 5, 1, 3, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [1, 1, 1, 0]]} "Class ", 2354, " is:" {{[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 5, 1, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 5, 1, 3, 4], [1, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 5, 1, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 5, 1, 3, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1265, 4148, 13808, 46542, 158534, 544869, 1887212, 6580775, 23083823, 81399079, 288380766, 1025982051, 3664054185] "" "Class ", 2355, " is:" {{[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 5, 1, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 5, 1, 3, 4], [1, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 5, 1, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 5, 1, 3, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 3}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 4}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [4, 3, 1, 2], {1, 2, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1211, 3875, 12548, 41040, 135370, 449791, 1504057, 5057668, 17092030, 58018150, 197727023, 676290905, 2320721255] "" "Class ", 2356, " is:" {{[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 5, 1, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 5, 1, 3, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [0, 1, 0, 1]]} "Class ", 2357, " is:" {{[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 5, 1, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 5, 1, 3, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [1, 1, 0, 1]]} "Class ", 2358, " is:" {{[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 5, 1, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 5, 1, 3, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 5, 1, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 5, 1, 3, 4], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {[0, 1, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1221, 3939, 12886, 42648, 142544, 480459, 1631287, 5574073, 19153815, 66146259, 229452587, 799140681, 2793373937] "" "Class ", 2359, " is:" {{[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 5, 1, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 5, 1, 3, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [1, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 5, 1, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 5, 1, 3, 4], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 3}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {[0, 1, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 2360, " is:" {{[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 5, 1, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 5, 1, 3, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [0, 1, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 1, 5, 3, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 5, 1, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 5, 1, 3, 4], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 3, 1, 5, 2], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {[0, 1, 0, 1]}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1], [0, 1, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105996, 330618, 1032663, 3228944, 10105023, 31645837, 99161410, 310865491, 974927593] "" "Class ", 2361, " is:" {{[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 5, 2, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 3, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 5, 2, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 3, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 5, 3, 2], {1, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 2, 5, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 127, 409, 1355, 4589, 15808, 55210, 195035, 695631, 2501567, 9060052, 33017590, 120986491, 445491925, 1647521977, 6116764262] "" "Class ", 2362, " is:" {{[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 5, 2, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 3, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 5, 2, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 3, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 403, 1329, 4488, 15436, 53865, 190193, 678174, 2438380, 8830272, 32178035, 117905067, 434134214, 1605494762, 5960687462] "" "Class ", 2363, " is:" {{[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 5, 2, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 3, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [0, 1, 0, 0]]} "Class ", 2364, " is:" {{[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 5, 2, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 3, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [1, 1, 0, 0]]} "Class ", 2365, " is:" {{[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 5, 2, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 3, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [0, 0, 1, 0]]} "Class ", 2366, " is:" {{[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 5, 2, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 3, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [1, 0, 1, 0]]} "Class ", 2367, " is:" {{[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 5, 2, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 3, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [0, 1, 1, 0]]} "Class ", 2368, " is:" {{[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 5, 2, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 3, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [1, 1, 1, 0]]} "Class ", 2369, " is:" {{[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 5, 2, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 3, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 5, 2, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 3, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}] , [[4, 3, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4159, 13883, 46959, 160608, 554500, 1929947, 6764488, 23855708, 84587419, 301380544, 1078453368, 3874161462] "" "Class ", 2370, " is:" {{[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 5, 2, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 3, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 5, 2, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 3, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}] , [[4, 3, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1211, 3875, 12548, 41040, 135370, 449791, 1504057, 5057668, 17092030, 58018150, 197727023, 676290905, 2320721255] "" "Class ", 2371, " is:" {{[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 5, 2, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 3, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [0, 1, 0, 1]]} "Class ", 2372, " is:" {{[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 5, 2, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 3, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [1, 1, 0, 1]]} "Class ", 2373, " is:" {{[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 5, 2, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 3, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 5, 2, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 3, 5], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {[0, 1, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 376, 1167, 3668, 11652, 37351, 120668, 392493, 1284289, 4224616, 13962275, 46340301, 154388659, 516144330, 1730980524] "" "Class ", 2374, " is:" {{[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 5, 2, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 3, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [1, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 5, 2, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 3, 5], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {2}, {[0, 1, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 366, 1105, 3356, 10251, 31483, 97186, 301431, 939004, 2936896, 9219531, 29040111, 91757034, 290754383, 923769926] "" "Class ", 2375, " is:" {{[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 5, 2, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 3, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [0, 1, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 2, 5, 3, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 5, 2, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 4, 1, 3, 5], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 3, 1, 4, 2], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {2}, {[0, 1, 1, 0]}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 1, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 120, 345, 972, 2691, 7348, 19855, 53230, 141871, 376466, 995705, 2627018, 6918101, 18192804, 47791365, 125443416] "" "Class ", 2376, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 1, 4, 3, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 5, 2, 3, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 1, 4, 3, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 5, 2, 3, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {1}, {}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [4, 2, 1, 5, 3], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 3, 1, 5, 2], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1265, 4151, 13833, 46687, 159260, 548215, 1901892, 6643137, 23342857, 82457708, 292654938, 1043078724, 3731944101] "" "Class ", 2377, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 1, 4, 3, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 5, 2, 3, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 1, 4, 3, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 5, 2, 3, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 4}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 368, 1125, 3482, 10902, 34498, 110221, 355216, 1153656, 3772657, 12412983, 41065128, 136516794, 455823009, 1527969136] "" "Class ", 2378, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 1, 4, 3, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 5, 2, 3, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 1, 4, 3, 2], [0, 1, 0, 0]]} "Class ", 2379, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 5, 2, 3, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 5, 2, 3, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1, 5], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 4}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {1}, {[0, 1, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 361, 1094, 3368, 10519, 33269, 106362, 343193, 1116188, 3655336, 12043017, 39889065, 132747674, 443648571, 1488358040] "" "Class ", 2380, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 1, 4, 3, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 5, 2, 3, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 1]], [[5, 1, 4, 3, 2], [0, 0, 1, 0]]} "Class ", 2381, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 1, 4, 3, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 5, 2, 3, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 1, 4, 3, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 5, 2, 3, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1, 5], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 2, 1, 4], {1, 2, 4}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {1}, {}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 3, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0]}] , [[4, 2, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 3, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 5, 2, 1], {2, 3}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 357, 1053, 3107, 9174, 27112, 80205, 237527, 704232, 2090332, 6211620, 18478575, 55027952, 164029803, 489393322] "" "Class ", 2382, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 1, 4, 3, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 5, 2, 3, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 1, 4, 3, 2], [0, 1, 1, 0]]} "Class ", 2383, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 1, 4, 3, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 5, 2, 3, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [0, 1, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 1, 4, 3, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 5, 2, 3, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1, 5], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 2, 1, 4], {1, 2, 4}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {1}, {[0, 1, 0, 0, 1]}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 3, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0]}] , [[4, 2, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 3, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 5, 2, 1], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 120, 349, 1014, 2954, 8638, 25350, 74626, 220262, 651562, 1931101, 5732981, 17044898, 50742594, 151234892, 451209163] "" "Class ", 2384, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 1, 4, 3, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 5, 2, 3, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 1, 4, 3, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 5, 2, 3, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 3}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [4, 3, 1, 2], {1, 2, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 2, 1, 5, 3], {1, 2, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 3, 1, 5, 2], {1, 2, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1213, 3893, 12658, 41601, 137968, 461131, 1551671, 5252218, 17871292, 61092824, 209718021, 722626830, 2498458052] "" "Class ", 2385, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 1, 4, 3, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 5, 2, 3, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 1, 4, 3, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 5, 2, 3, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 3}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 4}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [4, 3, 1, 2], {1, 2, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 356, 1042, 3037, 8827, 25618, 74315, 215632, 626120, 1819845, 5295578, 15428589, 45006923, 131450682, 384376649] "" "Class ", 2386, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 1, 4, 3, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 5, 2, 3, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 1, 4, 3, 2], [0, 1, 0, 1]]} "Class ", 2387, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 5, 2, 3, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [1, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 5, 2, 3, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1, 5], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 3}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 4}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [4, 3, 1, 2], {1, 2, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 1, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 120, 348, 1002, 2876, 8253, 23717, 68306, 197200, 570671, 1655112, 4810025, 14004288, 40840413, 119279153, 348837048] "" "Class ", 2388, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 1, 4, 3, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 5, 2, 3, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [1, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 1, 4, 3, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 5, 2, 3, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1, 5], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 2, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [4, 2, 1, 5, 3], {1, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 3, 1, 5, 2], {1, 2, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 376, 1167, 3665, 11617, 37102, 119252, 385386, 1251307, 4079515, 13348068, 43814637, 144233139, 476027908, 1574765316] "" "Class ", 2389, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 1, 4, 3, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 5, 2, 3, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 1, 4, 3, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 5, 2, 3, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1, 5], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 4}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 2, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 120, 345, 972, 2691, 7348, 19855, 53230, 141871, 376466, 995705, 2627018, 6918101, 18192804, 47791365, 125443416] "" "Class ", 2390, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 1, 4, 3, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 5, 2, 3, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 1, 4, 3, 2], [0, 1, 1, 1]]} "Class ", 2391, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 5, 3, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 5, 4], [0, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 5, 3, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 5, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [4, 2, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 3, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 128, 415, 1382, 4697, 16226, 56797, 201002, 717970, 2585066, 9372151, 34185178, 125360624, 461906052, 1709227519, 6349161702] "" "Class ", 2392, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 5, 3, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 5, 4], [0, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 5, 3, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 5, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4157, 13863, 46827, 159886, 550943, 1913526, 6691891, 23544320, 83280751, 295986327, 1056461081, 3785365874] "" "Class ", 2393, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 5, 3, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 5, 4], [0, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 5, 3, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 5, 4], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 383, 1199, 3782, 11973, 37947, 120224, 380422, 1201695, 3788572, 11919871, 37426762, 117281557, 366816085, 1145193604] "" "Class ", 2394, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 5, 3, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 5, 4], [0, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 5, 3, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 5, 4], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {4}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 364, 1083, 3207, 9448, 27699, 80852, 235108, 681452, 1969772, 5680771, 16352470, 46999847, 134920919, 386943529] "" "Class ", 2395, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 5, 3, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 5, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 0, 1, 0]]} "Class ", 2396, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 5, 3, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 5, 4], [0, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [1, 0, 1, 0]]} "Class ", 2397, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 5, 3, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 5, 4], [0, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 1, 1, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 5, 3, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 5, 4], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 373, 1136, 3462, 10538, 32010, 96997, 293191, 884106, 2660077, 7987470, 23940983, 71644479, 214099942, 639030894] "" "Class ", 2398, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 5, 3, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 5, 4], [0, 1, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [1, 1, 1, 0]]} "Class ", 2399, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 5, 3, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 5, 4], [1, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 5, 3, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 5, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [3, 1, 4, 2], {1, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [4, 2, 5, 1, 3], {1, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 3, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 127, 409, 1355, 4588, 15803, 55190, 194960, 695359, 2500587, 9056520, 33004821, 120940129, 445322830, 1646902490, 6114485110] "" "Class ", 2400, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 5, 3, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 5, 4], [1, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 5, 3, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 5, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [3, 1, 4, 2], {1, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {1, 3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1213, 3895, 12678, 41738, 138740, 465015, 1569820, 5332874, 18217152, 62537382, 215632129, 746466095, 2593374279] "" "Class ", 2401, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 5, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 5, 4], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [3, 5, 1, 4, 2], {5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1155, 3576, 11089, 34360, 106246, 327646, 1007510, 3089375, 9448172, 28825991, 87758721, 266669685, 808974393] "" "Class ", 2402, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 5, 3, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 5, 4], [1, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [1, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 5, 3, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 5, 4], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {4}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 354, 1021, 2901, 8130, 22513, 61713, 167746, 452789, 1215197, 3246050, 8637641, 22912633, 60624546, 160075117] "" "Class ", 2403, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 5, 3, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 5, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 5, 3, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 5, 4], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 2, 0, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4158, 13873, 46893, 160247, 552723, 1921756, 6728347, 23701026, 83939765, 298712615, 1067598164, 3830414563] "" "Class ", 2404, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 5, 3, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 5, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [1, 0, 1, 1]]} "Class ", 2405, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 5, 3, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 5, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 1, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 5, 3, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 5, 4], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1], [0, 2, 0, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 2, 0, 0, 0]}], [ [3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1], [0, 0, 2, 0, 0], [0, 1, 1, 0, 0], [0, 2, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 364, 1082, 3195, 9362, 27219, 78548, 225112, 641108, 1815509, 5115038, 14345261, 40066286, 111490948, 309205838] "" "Class ", 2406, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 5, 3, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 5, 3, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [4, 2, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 3, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1268, 4176, 13978, 47401, 162485, 562110, 1960062, 6882053, 24310783, 86338852, 308094471, 1104120529, 3972108041] "" "Class ", 2407, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 5, 3, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 5, 3, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 368, 1128, 3519, 11163, 35933, 117101, 385592, 1280894, 4287267, 14444471, 48947211, 166713704, 570414987, 1959673045] "" "Class ", 2408, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 5, 3, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 5, 3, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4, 5], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, %2], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1}, %3], [[2, 4, 3, 1], {1}, %3], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1}, %2], [[3, 2, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, %2], [[4, 2, 1, 3], {}, %3], [[4, 2, 3, 1], {3}, %3], [[4, 3, 1, 2], {}, %2], [[4, 3, 2, 1], {3}, {}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 2, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {1, 2}, %1], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[5, 2, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2}, %1], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 3, 2, 4, 1], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 3}, %1]} %1 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]} %2 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]} %3 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 357, 1046, 3044, 8799, 25289, 72332, 206076, 585289, 1658314, 4690093, 13247760, 37389101, 105476595, 297521218] "" "Class ", 2409, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 5, 3, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 5, 3, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4, 5], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [ [3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 2, 0, 0, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 119, 339, 950, 2629, 7212, 19674, 53506, 145359, 395062, 1075374, 2934103, 8028839, 22041610, 60719642, 167856949] "" "Class ", 2410, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 5, 3, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 0, 1, 0]]} "Class ", 2411, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 5, 3, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [1, 0, 1, 0]]} "Class ", 2412, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 5, 3, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 1, 1, 0]]} "Class ", 2413, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 5, 3, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 0]]} "Class ", 2414, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 5, 3, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 5, 3, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [3, 1, 4, 2], {1, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [4, 2, 5, 1, 3], {1, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 3, 5, 1, 2], {1, 2, 3, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1213, 3893, 12658, 41601, 137968, 461131, 1551671, 5252218, 17871292, 61092824, 209718021, 722626830, 2498458052] "" "Class ", 2415, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 5, 3, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 5, 3, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [3, 1, 4, 2], {1, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 358, 1067, 3214, 9788, 30111, 93469, 292469, 921637, 2922470, 9318414, 29858927, 96100247, 310529452, 1007036638] "" "Class ", 2416, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 5, 3, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 5, 3, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, %2], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1}, %1], [[2, 4, 3, 1], {1}, %1], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1}, %2], [[3, 2, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, %2], [[4, 2, 1, 3], {}, %1], [[4, 2, 3, 1], {3}, %1], [[4, 3, 1, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 2, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 3, 1, 5, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[5, 2, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [5, 3, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 3, 2, 4, 1], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} %1 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]} %2 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 120, 346, 977, 2704, 7351, 19682, 52029, 136085, 352816, 908047, 2322856, 5911867, 14982006, 37830980, 95234431] "" "Class ", 2417, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 5, 3, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [1, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 5, 3, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4, 5], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [ [3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 2, 0, 0, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 118, 326, 864, 2210, 5492, 13334, 31768, 74522, 172572, 395294, 897056, 2019362, 4513828, 10027046, 22151208] "" "Class ", 2418, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 5, 3, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 5, 3, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4, 5], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {[0, 2, 0, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [ [2, 4, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 2, 0, 0], [0, 1, 1, 0, 0], [0, 2, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 356, 1045, 3062, 8968, 26267, 76968, 225652, 661931, 1942761, 5704820, 16759445, 49255243, 144811063, 425883398] "" "Class ", 2419, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 5, 3, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [1, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 5, 3, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4, 5], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {2}, {[0, 2, 0, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [ [2, 4, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 2, 0, 0], [0, 1, 1, 0, 0], [0, 2, 0, 0, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [ [4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 2, 0, 0], [0, 1, 1, 0, 0], [0, 2, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 118, 328, 881, 2300, 5874, 14758, 36639, 90189, 220671, 537659, 1306173, 3166813, 7667395, 18546734, 44834456] "" "Class ", 2420, " is:" {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 5, 3, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 5, 3, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4, 5], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {[0, 2, 0, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, %1], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 2, 0, 0], [0, 1, 1, 0, 0], [0, 2, 0, 0, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1}, %1], [[3, 2, 1, 4], {}, {[0, 0, 0, 0, 1], [0, 2, 0, 0, 0]}], [[3, 2, 4, 1], {3}, {[0, 0, 0, 0, 1], [0, 2, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, %1], [[4, 2, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 2, 0, 0, 0]}], [[4, 2, 3, 1], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 2, 0, 0, 0]}], [ [4, 3, 1, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {[0, 0, 2, 0, 0], [0, 1, 1, 0, 0], [0, 2, 0, 0, 0]}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 2, 0, 0, 0, 0]}], [[4, 2, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 2, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 2, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 2, 0, 0, 0, 0]}], [[5, 2, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 2, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 2, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 2, 0, 0, 0, 0]}]} %1 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 118, 326, 860, 2175, 5304, 12545, 28924, 65284, 144752, 316189, 682002, 1455377, 3077570, 6457434, 13459100] "" "Class ", 2421, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 5, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 3, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 5, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 3, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 127, 410, 1360, 4608, 15878, 55462, 195940, 698893, 2513369, 9102944, 33174186, 121560729, 447606438, 1655338567, 6145763870] "" "Class ", 2422, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 5, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 3, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 5, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 3, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [3, 4, 1, 2], {1, 2, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 404, 1335, 4513, 15531, 54212, 191441, 682654, 2454510, 8888615, 32390133, 118679945, 436978338, 1615978858, 5999487372] "" "Class ", 2423, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 5, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 3, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [0, 1, 0, 0]]} "Class ", 2424, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 5, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 3, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [1, 1, 0, 0]]} "Class ", 2425, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 5, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 3, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [0, 0, 1, 0]]} "Class ", 2426, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [3, 5, 1, 4, 2], {5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 376, 1167, 3662, 11570, 36683, 116436, 369439, 1170693, 3703226, 11691221, 36834572, 115819092, 363468805, 1138571922] "" "Class ", 2427, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 5, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 3, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [0, 1, 1, 0]]} "Class ", 2428, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 5, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 3, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 5, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 3, 5], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1], [0, 1, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1032, 2973, 8496, 24111, 68017, 190885, 533294, 1484021, 4115186, 11375765, 31358377, 86223943, 236540916] "" "Class ", 2429, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 5, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 3, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 5, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 3, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 394, 1273, 4194, 14039, 47614, 163266, 565072, 1971476, 6926313, 24482914, 87009495, 310710172, 1114326403, 4011922558] "" "Class ", 2430, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 5, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 3, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 5, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 3, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1220, 3929, 12822, 42309, 140922, 473169, 1599864, 5442561, 18615176, 63975857, 220816906, 765121477, 2660426630] "" "Class ", 2431, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 5, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 3, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [0, 1, 0, 1]]} "Class ", 2432, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 5, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 3, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [1, 1, 0, 1]]} "Class ", 2433, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 5, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 3, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 5, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 3, 5], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 376, 1168, 3676, 11689, 37474, 120943, 392508, 1279859, 4190153, 13766425, 45368183, 149923601, 496652029, 1648895407] "" "Class ", 2434, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 5, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 3, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 5, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 3, 5], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 364, 1082, 3195, 9362, 27219, 78548, 225112, 641108, 1815509, 5115038, 14345261, 40066286, 111490948, 309205838] "" "Class ", 2435, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 5, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 3, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [0, 1, 1, 1]]} "Class ", 2436, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 5, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 4, 3, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 2, 3, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 1]], [[5, 3, 4, 1, 2], [1, 1, 1, 1]]} "Class ", 2437, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 5, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 5, 4], [1, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 5, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 5, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4157, 13863, 46827, 159886, 550943, 1913526, 6691891, 23544320, 83280751, 295986327, 1056461081, 3785365874] "" "Class ", 2438, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 5, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 5, 4], [0, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 5, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 5, 4], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {4}, %1], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 1, 4], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 5, 2, 1, 3], {3}, %1], [[4, 5, 2, 3, 1], {3}, %1], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {[0, 0, 0, 0, 0, 1]}]} %1 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1217, 3890, 12524, 40533, 131723, 429525, 1404685, 4605654, 15136513, 49854805, 164540794, 544093171, 1802435738] "" "Class ", 2439, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 5, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 5, 4], [1, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 5, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 5, 4], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 366, 1106, 3367, 10326, 31897, 99218, 310677, 978870, 3101972, 9881982, 31633487, 101709806, 328338801, 1063829240] "" "Class ", 2440, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 5, 4], [1, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 5, 4], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 356, 1043, 3045, 8864, 25739, 74577, 215664, 622591, 1794573, 5165624, 14850779, 42647577, 122350480, 350691479] "" "Class ", 2441, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 5, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 5, 4], [1, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 5, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 5, 4], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 120, 345, 972, 2691, 7348, 19855, 53230, 141871, 376466, 995705, 2627018, 6918101, 18192804, 47791365, 125443416] "" "Class ", 2442, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 5, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 5, 4], [1, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 1]], [[4, 5, 3, 1, 2], [1, 1, 0, 1]]} "Class ", 2443, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 5, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 5, 4], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [4, 5, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 5, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 5, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1265, 4151, 13833, 46687, 159260, 548215, 1901892, 6643137, 23342857, 82457708, 292654938, 1043078724, 3731944101] "" "Class ", 2444, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 5, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 5, 4], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 368, 1128, 3519, 11163, 35933, 117101, 385592, 1280894, 4287267, 14444471, 48947211, 166713704, 570414987, 1959673045] "" "Class ", 2445, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 5, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 5, 4], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4, 5], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, %3], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1}, %4], [[2, 4, 3, 1], {1}, %4], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1}, %3], [[3, 2, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, %3], [[4, 2, 1, 3], {}, %4], [[4, 2, 3, 1], {3}, %4], [[4, 3, 1, 2], {}, %3], [[4, 3, 2, 1], {}, {}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, %2], [[2, 5, 4, 3, 1], {1}, %1], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 2, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {1, 2}, %1], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {4}, %2], [[4, 3, 2, 1, 5], {3}, {[0, 0, 0, 0, 0, 1]}], [[4, 3, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[5, 2, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2}, %1], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {4}, %2], [[5, 3, 2, 1, 4], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 3, 2, 4, 1], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {4}, %2], [[5, 4, 2, 1, 3], {3}, %1], [[5, 4, 2, 3, 1], {3}, %1], [[5, 4, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {3}, {}]} %1 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]} %2 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]} %3 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]} %4 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 359, 1071, 3221, 9773, 29919, 92385, 287575, 901782, 2846712, 9040255, 28863115, 92595858, 298342901, 965011641] "" "Class ", 2446, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 5, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 5, 4], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4, 5], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [ [3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 2, 0, 0, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 119, 341, 980, 2857, 8473, 25520, 77869, 240215, 747976, 2347759, 7420373, 23595070, 75427289, 242264554, 781428353] "" "Class ", 2447, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 5, 4], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]} "Class ", 2448, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 118, 330, 903, 2437, 6504, 17213, 45249, 118303, 307910, 798368, 2063347, 5317629, 13670636, 35067411, 89776013] "" "Class ", 2449, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 5, 4], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 0]]} "Class ", 2450, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 5, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 5, 4], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4, 5], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 2, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1], [0, 2, 0, 0, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 116, 310, 796, 1984, 4832, 11552, 27200, 63232, 145408, 331264, 748544, 1679360, 3743744, 8298496, 18300928] "" "Class ", 2451, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]} {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 2, 1, 4], {1, 2}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {1}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 5, 4, 3, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 358, 1059, 3151, 9434, 28405, 86036, 261933, 801084, 2460283, 7583967, 23456295, 72768717, 226374769, 706006982] "" "Class ", 2452, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]} {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, %1], [[2, 4, 3, 1], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {1, 2}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, %1], [[4, 2, 1, 3], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1}, %1], [[4, 3, 2, 1], {2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 5, 4, 3, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 1, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 3, 2], {1}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 2, 4, 3, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} %1 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 118, 328, 880, 2296, 5865, 14761, 36776, 91043, 224547, 552802, 1360081, 3346846, 8240999, 20309872, 50103441] "" "Class ", 2453, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, %2], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1}, %3], [[2, 4, 3, 1], {1}, %3], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1}, %2], [[3, 2, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, %2], [[4, 2, 1, 3], {}, %3], [[4, 2, 3, 1], {3}, %3], [[4, 3, 1, 2], {}, %2], [[4, 3, 2, 1], {3}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, %1], [[2, 5, 4, 3, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 2, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {4}, %1], [[4, 3, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[5, 2, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {4}, %1], [[5, 3, 2, 4, 1], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {4}, %1], [[5, 4, 2, 3, 1], {1, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} %1 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]} %2 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]} %3 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 117, 316, 808, 1973, 4643, 10617, 23749, 52241, 113459, 244022, 520886, 1105312, 2334380, 4911136, 10299060] "" "Class ", 2454, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 5, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 5, 4], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4, 5], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, %3], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1}, %4], [[2, 4, 3, 1], {1}, %4], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1}, %3], [[3, 2, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, %3], [[4, 2, 1, 3], {2}, %4], [[4, 2, 3, 1], {2}, %4], [[4, 3, 1, 2], {}, %3], [[4, 3, 2, 1], {3}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, %2], [[2, 5, 4, 3, 1], {1, 2}, %1], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 1, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 2, 5, 1, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {4}, %2], [[4, 3, 2, 5, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [[4, 3, 5, 1, 2], {3}, %2], [[4, 3, 5, 2, 1], {4}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 3, 2], {1}, %2], [[5, 2, 4, 3, 1], {1, 2}, %1], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1}, %2], [[5, 4, 2, 3, 1], {1, 3}, %1]} %1 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]} %2 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]} %3 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]} %4 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 115, 296, 699, 1531, 3146, 6124, 11381, 20318, 35018, 58501, 95048, 150606, 233287, 353975, 527056] "" "Class ", 2455, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 5, 4], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]} "Class ", 2456, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 5, 4], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]} "Class ", 2457, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 5, 4], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 1]]} "Class ", 2458, " is:" {{[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 5, 4], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]} "Class ", 2459, " is:" {{[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 3, 2], {1, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 2, 4, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1268, 4173, 13955, 47278, 161942, 559895, 1951374, 6848546, 24182943, 85854641, 306270741, 1097277991, 3946501425] "" "Class ", 2460, " is:" {{[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1213, 3894, 12667, 41654, 138223, 462235, 1556168, 5269877, 17939014, 61348388, 210671442, 726154020, 2511425918] "" "Class ", 2461, " is:" {{[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3, 5], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 2, 1, 4], {2}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {2}, {}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 2, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 3, 5, 1, 2], {1, 2, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[5, 2, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {2, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [5, 3, 1, 4, 2], {1, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 3, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 367, 1117, 3438, 10683, 33461, 105530, 334859, 1068333, 3424956, 11027792, 35646926, 115637003, 376335371, 1228390033] "" "Class ", 2462, " is:" {{[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [1, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3, 5], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 2, 1, 4], {2}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {2}, {}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 2, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 3, 5, 1, 2], {1, 2, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[5, 2, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {2, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [5, 3, 1, 4, 2], {1, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 3, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 367, 1117, 3438, 10683, 33461, 105530, 334859, 1068333, 3424956, 11027792, 35646926, 115637003, 376335371, 1228390033] "" "Class ", 2463, " is:" {{[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [0, 0, 1, 0]]} "Class ", 2464, " is:" {{[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [1, 0, 1, 0]]} "Class ", 2465, " is:" {{[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [0, 1, 1, 0]]} "Class ", 2466, " is:" {{[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [1, 1, 1, 0]]} "Class ", 2467, " is:" {{[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 3, 2], {1, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 2, 4, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 376, 1170, 3704, 11912, 38835, 128071, 426439, 1431518, 4839205, 16458985, 56282864, 193392667, 667391510, 2312144889] "" "Class ", 2468, " is:" {{[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 364, 1083, 3208, 9461, 27800, 81460, 238237, 695924, 2031720, 5930864, 17317089, 50587384, 147874414, 432587166] "" "Class ", 2469, " is:" {{[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 2, 1, 4], {2}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[4, 3, 1, 2], {1, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {2}, {}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [4, 2, 5, 1, 3], {1, 2, 3, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0]}], [[4, 3, 5, 1, 2], {1, 2, 5}, { [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 120, 343, 950, 2549, 6644, 16883, 41970, 102385, 245744, 581615, 1359854, 3145709, 7208940, 16383979, 36962282] "" "Class ", 2470, " is:" {{[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3, 5], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 1, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {1, 2}, { [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 1, 0, 0], [0, 1, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 120, 343, 950, 2549, 6644, 16883, 41970, 102385, 245744, 581615, 1359854, 3145709, 7208940, 16383979, 36962282] "" "Class ", 2471, " is:" {{[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [0, 0, 1, 1]]} "Class ", 2472, " is:" {{[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [1, 0, 1, 1]]} "Class ", 2473, " is:" {{[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [0, 1, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3, 5], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 2, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[4, 3, 1, 2], {1, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {2}, {[0, 1, 0, 1, 0]}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [4, 2, 1, 5, 3], {1, 2, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {1, 2, 3, 5}, { [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {1, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 2, 5, 1], {2}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 0, 0]}], [ [4, 3, 5, 1, 2], {1, 2, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 118, 321, 816, 1946, 4396, 9509, 19898, 40643, 81650, 162325, 320868, 632796, 1247912, 2464153, 4875182] "" "Class ", 2474, " is:" {{[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [1, 1, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3, 5], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 3, 2, 4, 1], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 2, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[4, 3, 1, 2], {1, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {2}, {[0, 1, 0, 1, 0]}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [4, 2, 1, 5, 3], {1, 2, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {1, 2, 3, 5}, { [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {1, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 2, 5, 1], {2}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 0, 0]}], [ [4, 3, 5, 1, 2], {1, 2, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 118, 321, 816, 1946, 4396, 9509, 19898, 40643, 81650, 162325, 320868, 632796, 1247912, 2464153, 4875182] "" "Class ", 2475, " is:" {{[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 3, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 4, 5], [0, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 3, 1], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3, 5], [0, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 4, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 2, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [5, 3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 3, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4155, 13845, 46717, 159318, 548258, 1901521, 6640186, 23327411, 82387974, 292363588, 1041918705, 3727476522] "" "Class ", 2476, " is:" {{[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 3, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 4, 5], [0, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 3, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3, 5], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 4, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 378, 1189, 3811, 12399, 40851, 136047, 457251, 1549018, 5284009, 18134866, 62575631, 216961551, 755496017, 2641005395] "" "Class ", 2477, " is:" {{[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 4, 5], [0, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3, 5], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 4, 5], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, %2], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1}, %3], [[2, 4, 3, 1], {1}, %3], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1}, %2], [[3, 2, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, %2], [[4, 2, 1, 3], {}, %3], [[4, 2, 3, 1], {3}, %3], [[4, 3, 1, 2], {}, %2], [[4, 3, 2, 1], {3}, {}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 2, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {1, 2}, %1], [[4, 3, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[5, 2, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2}, %1], [[5, 3, 2, 4, 1], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2}, %1], [[5, 4, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} %1 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]} %2 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]} %3 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 370, 1141, 3568, 11279, 35957, 115414, 372565, 1208492, 3936365, 12868539, 42204888, 138818065, 457776567, 1513140136] "" "Class ", 2478, " is:" {{[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 4, 5], [0, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3, 5], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 4, 5], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [ [4, 2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 2, 0, 0, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 361, 1094, 3366, 10477, 32887, 103933, 330420, 1056079, 3391496, 10937686, 35408772, 115024744, 374828719, 1224951087] "" "Class ", 2479, " is:" {{[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 3, 1], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 4, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 1, 0, 0]]} {[[1, 2, 3], [1, 1]], [[5, 4, 2, 3, 1], [0, 0, 1, 0]]} "Class ", 2480, " is:" {{[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 3, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3, 5], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 4, 5], [0, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 1, 0, 1]]} {[[1, 2, 3], [1, 1]], [[5, 4, 2, 3, 1], [1, 0, 1, 0]]} "Class ", 2481, " is:" {{[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 3, 1], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3, 5], [0, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 4, 5], [0, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 1, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 4, 2, 3, 1], [0, 1, 1, 0]]} "Class ", 2482, " is:" {{[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 3, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3, 5], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 4, 5], [0, 1, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 1]], [[5, 4, 2, 3, 1], [1, 1, 1, 0]]} "Class ", 2483, " is:" {{[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 3, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 4, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 3, 1], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 4, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 2, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [5, 3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 3, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1213, 3894, 12667, 41654, 138223, 462235, 1556168, 5269877, 17939014, 61348388, 210671442, 726154020, 2511425918] "" "Class ", 2484, " is:" {{[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 4, 5], [1, 0, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3, 5], [1, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 4, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 366, 1107, 3378, 10396, 32241, 100686, 316452, 1000495, 3180420, 10160520, 32607783, 105081979, 339922940, 1103409597] "" "Class ", 2485, " is:" {{[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 4, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 4, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, %2], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1}, %1], [[2, 4, 3, 1], {1}, %1], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1}, %2], [[3, 2, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, %2], [[4, 2, 1, 3], {}, %1], [[4, 2, 3, 1], {3}, %1], [[4, 3, 1, 2], {1, 2, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 2, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 3, 1, 5, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[5, 2, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [5, 3, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 3, 2, 4, 1], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} %1 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]} %2 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 357, 1046, 3035, 8713, 24751, 69610, 193965, 535905, 1469249, 3999942, 10820375, 29101297, 77855227, 207284970] "" "Class ", 2486, " is:" {{[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 4, 5], [1, 0, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 4, 5], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [ [4, 2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 2, 0, 0, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 120, 346, 976, 2688, 7232, 19040, 49152, 124672, 311296, 766464, 1863680, 4481024, 10665984, 25157632, 58851328] "" "Class ", 2487, " is:" {{[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 1, 0, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 3, 1], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 4, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 1, 0, 0]]} {[[1, 2, 3], [1, 1]], [[5, 4, 2, 3, 1], [0, 0, 1, 1]]} "Class ", 2488, " is:" {{[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 3, 1], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 4, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 1, 0, 1]]} {[[1, 2, 3], [1, 1]], [[5, 4, 2, 3, 1], [1, 0, 1, 1]]} "Class ", 2489, " is:" {{[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 3, 1], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 4, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 4, 2, 3, 1], [0, 1, 1, 1]]} "Class ", 2490, " is:" {{[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 2, 3, 1], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3, 5], [1, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 3, 2, 4, 5], [1, 1, 1, 1]]}} {[[1, 2, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 1]], [[5, 4, 2, 3, 1], [1, 1, 1, 1]]} "Class ", 2491, " is:" {{[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 2, 1, 4], {1, 2}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 117, 325, 881, 2374, 6477, 17699, 48763, 135538, 377416, 1058122, 2979556, 8411634, 23860656, 67863592, 193534817] "" "Class ", 2492, " is:" {{[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]} {[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]} "Class ", 2493, " is:" {{[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 0]]}} {[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]} {[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]} "Class ", 2494, " is:" {{[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, %1], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1}, %2], [[2, 4, 3, 1], {1}, %2], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1}, %1], [[3, 2, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, %1], [[4, 2, 1, 3], {}, %2], [[4, 2, 3, 1], {3}, %2], [[4, 3, 1, 2], {}, %1], [[4, 3, 2, 1], {3}, {[1, 0, 0, 0, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[2, 5, 4, 3, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 2, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[5, 2, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 3, 2, 4, 1], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0]}]} %1 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]} %2 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 112, 266, 537, 917, 1382, 1956, 2692, 3617, 4760, 6152, 7826, 9817, 12162, 14900, 18072] "" "Class ", 2495, " is:" {{[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 0]]}} {[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]} {[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]} "Class ", 2496, " is:" {{[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]}} {[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]} {[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]}, {[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]}, {[[3, 2, 1], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, %3], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1}, %4], [[2, 4, 3, 1], {1}, %4], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1}, %3], [[3, 2, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, %3], [[4, 2, 1, 3], {2}, %4], [[4, 2, 3, 1], {2}, %4], [[4, 3, 1, 2], {}, %3], [[4, 3, 2, 1], {3}, {[1, 0, 0, 0, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {1, 2, 3, 4, 5}, %2], [[2, 5, 4, 3, 1], {1, 2}, %1], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 1, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 2, 5, 1, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 2, 5, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [ [4, 3, 5, 1, 2], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 3, 5, 2, 1], {4}, {[0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 3, 2], {1, 2, 3, 4, 5}, %2], [[5, 2, 4, 3, 1], {1, 2}, %1], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, %2], [[5, 4, 2, 3, 1], {1, 3}, %1]} %1 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0]} %2 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]} %3 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]} %4 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 109, 235, 379, 405, 282, 89, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 2497, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 2, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4}, {}], [[1, 3, 4, 5, 2], {1, 2, 3, 4}, {}], [[2, 3, 4, 5, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 286, 1530, 9344, 64150, 489268, 4104364, 37560264, 372363032, 3975471036, 45475045972, 554863724760, 7193302728580, 98740185161408, 1430673767067448, 21820449121179712] "" "Class ", 2498, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2}, {[0, 0, 0, 0, 1]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 283, 1489, 8876, 59103, 434827, 3502407, 30651877, 289613409, 2938111458, 31852622144, 367493142740, 4495632904533, 58124360058441, 791932909143889, 11340829044968869] "" "Class ", 2499, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 2, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 3, 5, 4], {3}, {}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {3}, {}], [[1, 2, 5, 3, 4], {3}, {}], [[1, 2, 5, 4, 3], {3}, {}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {3}, {}], [[1, 3, 5, 2, 4], {3, 4}, {}], [[1, 3, 5, 4, 2], {3}, {}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {}], [[1, 4, 5, 3, 2], {3}, {}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 5, 1], {3}, {}], [[2, 3, 5, 1, 4], {3, 4}, {}], [[2, 3, 5, 4, 1], {3}, {}], [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[2, 4, 5, 3, 1], {3}, {}], [[2, 5, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1490, 8818, 57896, 417458, 3277188, 27813798, 253710444, 2474725252, 25698141034, 282997659072, 3293701769556, 40391275488760, 520492097243776, 7030777642663656] "" "Class ", 2500, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4, 5], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4, 5], [1, 1, 0, 0]]} "Class ", 2501, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]} "Class ", 2502, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]} "Class ", 2503, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 1, 0]]} "Class ", 2504, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4, 5], [1, 1, 1, 0]]} "Class ", 2505, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 2, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {2}, {}], [[1, 3, 4, 2, 5], {2, 3}, {}], [[1, 3, 4, 5, 2], {2}, {}], [[1, 3, 5, 2, 4], {2, 3}, {}], [[1, 4, 5, 2, 3], {2, 3}, {}], [[1, 4, 5, 3, 2], {4}, {}], [[2, 3, 4, 5, 1], {1, 2, 3, 4}, {}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 286, 1520, 9174, 61840, 460222, 3747456, 33132382, 316056208, 3235516438, 35378942136, 411518093110, 5073476658132, 66083904325534, 906794920452808, 13074362903730190] "" "Class ", 2506, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 0, 1]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {}], [[1, 3, 5, 2, 4], {2, 3}, {}], [[1, 4, 5, 2, 3], {2, 3}, {}], [[1, 4, 5, 3, 2], {4}, {}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 283, 1479, 8687, 56389, 399938, 3070656, 25334216, 223280484, 2091531152, 20734826001, 216747865040, 2381374679376, 27421276260557, 330095237611052, 4144803045030802] "" "Class ", 2507, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {3}, {[0, 0, 0, 0, 1]}], [[1, 2, 4, 3], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 2, 5, 4, 3], {3}, {}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {3, 4}, {}], [[1, 3, 5, 4, 2], {3}, {}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {}], [[1, 4, 5, 3, 2], {3}, {}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3, 4}, {}], [[2, 3, 5, 4, 1], {3}, {}], [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[2, 4, 5, 3, 1], {3}, {}], [[2, 5, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1483, 8694, 56051, 393250, 2972512, 24033524, 206641813, 1880213660, 18031294285, 181621023288, 1915641357142, 21102116968802, 242206781291439, 2890622613962612] "" "Class ", 2508, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]} "Class ", 2509, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 1, 1]]} "Class ", 2510, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]} "Class ", 2511, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]} "Class ", 2512, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]} "Class ", 2513, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 292, 1561, 9435, 63528, 471685, 3827935, 33710784, 320215234, 3263470533, 35521211392, 411258574080, 5046683271858, 65430136131475, 893695739453843, 12826929093858046] "" "Class ", 2514, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]} "Class ", 2515, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 3, 4, 5], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 3, 2, 1], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 3, 4, 5], [1, 1, 0, 0]]} "Class ", 2516, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 0]]} "Class ", 2517, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 1, 0]]} "Class ", 2518, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 3, 4, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 3, 2, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 3, 4, 5], [1, 1, 1, 0]]} "Class ", 2519, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {}], [[1, 3, 5, 2, 4], {2, 3}, {}], [[1, 4, 5, 2, 3], {2, 3}, {}], [[1, 4, 5, 3, 2], {4}, {}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 292, 1561, 9385, 62425, 453661, 3566159, 30097529, 271045855, 2591520158, 26195658260, 278925375214, 3118630027130, 36513524317734, 446572491284584, 5692801819100616] "" "Class ", 2520, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]} "Class ", 2521, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 3, 4, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 3, 2, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 3, 4, 5], [1, 1, 0, 1]]} "Class ", 2522, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 5, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 3, 5, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 1]]} "Class ", 2523, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 5, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 3, 5, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 1, 1]]} "Class ", 2524, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 5, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 3, 4, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 3, 2, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 3, 5, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 3, 4, 5], [1, 1, 1, 1]]} "Class ", 2525, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 4, 3, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 2, 4, 5], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 4, 2, 1], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 2, 3, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 4, 3, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 2, 4, 5], [0, 1, 0, 0]]} "Class ", 2526, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 4, 3, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 2, 4, 5], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 4, 2, 1], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 2, 3, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 4, 3, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 2, 4, 5], [1, 1, 0, 0]]} "Class ", 2527, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 2, 4, 5], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 2, 4, 5], [0, 0, 1, 0]]} "Class ", 2528, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 0]]} "Class ", 2529, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 2, 4, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 4, 2, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 2, 4, 5], [0, 1, 1, 0]]} "Class ", 2530, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 2, 4, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 4, 2, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 2, 4, 5], [1, 1, 1, 0]]} "Class ", 2531, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 2, 4, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 4, 2, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 2, 4, 5], [0, 1, 0, 1]]} "Class ", 2532, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 2, 4, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 4, 2, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 2, 4, 5], [1, 1, 0, 1]]} "Class ", 2533, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 4, 3, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 2, 4, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 2, 3, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 4, 3, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 2, 4, 5], [0, 0, 1, 1]]} "Class ", 2534, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 1]]} "Class ", 2535, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 4, 3, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 2, 4, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 4, 2, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 2, 3, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 4, 3, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 2, 4, 5], [0, 1, 1, 1]]} "Class ", 2536, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 4, 3, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 2, 4, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 2, 3, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 4, 3, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 2, 4, 5], [1, 1, 1, 1]]} "Class ", 2537, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 2, 1], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 2, 1], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 2, 3, 4, 5], {1}, {}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {1, 2, 3, 4}, {}], [[2, 3, 4, 5, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1508, 9120, 61966, 467528, 3879214, 35109664, 344234188, 3634624368, 41117416568, 496157861632, 6361251215132, 86355235822112, 1237416363760652, 18664631288402304] "" "Class ", 2538, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {[0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 281, 1463, 8600, 56358, 407726, 3228498, 27780766, 258185767, 2577653147, 27515937547, 312763320389, 3771590295893, 48093947311311, 646605910615198, 9141636107002635] "" "Class ", 2539, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4, 5], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 2, 1], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4, 5], [0, 1, 0, 0]]} "Class ", 2540, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4, 5], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 2, 1], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4, 5], [1, 1, 0, 0]]} "Class ", 2541, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 2, 1], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 1, 0]]} "Class ", 2542, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 0]]} "Class ", 2543, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 2, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4, 5], [0, 1, 1, 0]]} "Class ", 2544, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 2, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4, 5], [1, 1, 1, 0]]} "Class ", 2545, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 2, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 2, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 2, 3, 4, 5], {2}, {}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 2, 5], {2, 3}, {}], [[1, 3, 4, 5, 2], {2}, {}], [[1, 3, 5, 2, 4], {2, 3}, {}], [[1, 4, 5, 2, 3], {2, 3}, {}], [[1, 4, 5, 3, 2], {4}, {}], [[2, 3, 4, 5, 1], {1, 2, 3, 4}, {}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1498, 8930, 59272, 433122, 3453612, 29834394, 277537524, 2765931570, 29398258892, 331928609954, 3967262708368, 50038907484506, 664177921623996, 9254027823230010] "" "Class ", 2546, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {}], [[1, 3, 5, 2, 4], {2, 3}, {}], [[1, 4, 5, 2, 3], {2, 3}, {}], [[1, 4, 5, 3, 2], {4}, {}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 281, 1453, 8385, 53179, 366387, 2718148, 21567627, 182033412, 1626889853, 15337655000, 152024716122, 1579663347031, 17163121990089, 194543892416456, 2295827292425141] "" "Class ", 2547, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 2, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4, 5], [0, 1, 0, 1]]} "Class ", 2548, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 2, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4, 5], [1, 1, 0, 1]]} "Class ", 2549, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 2, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 2, 1, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 1, 1]]} "Class ", 2550, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {}], [[1, 3, 5, 2, 4], {2, 3}, {}], [[1, 4, 5, 2, 3], {2, 3}, {}], [[1, 4, 5, 3, 2], {4}, {}], [[2, 3, 1, 4, 5], {1, 2}, {[0, 0, 0, 1, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 3, 1], {2, 3}, {}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 280, 1432, 8092, 49643, 326328, 2275957, 16716192, 128534897, 1029846440, 8564882032, 73701745990, 654437777998, 5982600189976, 56192183652353, 541340240049356] "" "Class ", 2551, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 2, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 2, 1, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4, 5], [0, 1, 1, 1]]} "Class ", 2552, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 2, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 2, 1, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 4, 5, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4, 5], [1, 1, 1, 1]]} "Class ", 2553, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 5, 3, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1, 4, 5], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 5, 2, 1], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 1, 3, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 5, 3, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 3, 1, 4, 5], [0, 1, 0, 0]]} "Class ", 2554, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 5, 3, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1, 4, 5], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 5, 2, 1], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 1, 3, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 5, 3, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 3, 1, 4, 5], [1, 1, 0, 0]]} "Class ", 2555, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 5, 2, 1], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 0]]} "Class ", 2556, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 0]]} "Class ", 2557, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1, 4, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 5, 2, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 3, 1, 4, 5], [0, 1, 1, 0]]} "Class ", 2558, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1, 4, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 5, 2, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 3, 1, 4, 5], [1, 1, 1, 0]]} "Class ", 2559, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1, 4, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 5, 2, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 3, 1, 4, 5], [0, 1, 0, 1]]} "Class ", 2560, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1, 4, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 5, 2, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 3, 1, 4, 5], [1, 1, 0, 1]]} "Class ", 2561, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 5, 3, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 5, 2, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 1, 3, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 5, 3, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 1]]} "Class ", 2562, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 5, 3, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 5, 3, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 1]]} "Class ", 2563, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 5, 3, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1, 4, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 5, 2, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 1, 3, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 5, 3, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 3, 1, 4, 5], [0, 1, 1, 1]]} "Class ", 2564, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 5, 3, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1, 4, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 5, 2, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 1, 3, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 5, 3, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 3, 1, 4, 5], [1, 1, 1, 1]]} "Class ", 2565, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 5, 4, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 1, 4, 5], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 5, 2, 1], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 1, 2, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 5, 4, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 2, 1, 4, 5], [0, 1, 0, 0]]} "Class ", 2566, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 5, 4, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 1, 4, 5], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 5, 2, 1], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 1, 2, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 5, 4, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 2, 1, 4, 5], [1, 1, 0, 0]]} "Class ", 2567, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 1, 4, 5], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 5, 2, 1], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[3, 2, 1, 4, 5], [0, 0, 1, 0]]} "Class ", 2568, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]} "Class ", 2569, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 1, 4, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 5, 2, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 2, 1, 4, 5], [0, 1, 1, 0]]} "Class ", 2570, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 1, 4, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 5, 2, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 2, 1, 4, 5], [1, 1, 1, 0]]} "Class ", 2571, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 1, 4, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 5, 2, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 2, 1, 4, 5], [0, 1, 0, 1]]} "Class ", 2572, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 1, 4, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 5, 2, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 2, 1, 4, 5], [1, 1, 0, 1]]} "Class ", 2573, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 1, 4, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 5, 2, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[3, 2, 1, 4, 5], [0, 0, 1, 1]]} "Class ", 2574, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]} "Class ", 2575, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 1, 4, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 5, 2, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 2, 1, 4, 5], [0, 1, 1, 1]]} "Class ", 2576, " is:" {{[[1, 3, 2], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 5, 2, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]} "Class ", 2577, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 2, 4, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3, 5], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 2, 3, 1], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 4, 2, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 2, 4, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3, 5], [0, 0, 1, 0]]} "Class ", 2578, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 2, 4, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 4, 2, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 2, 4, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 1, 0]]} "Class ", 2579, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 2, 4, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 4, 2, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 2, 4, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 1, 0]]} "Class ", 2580, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 2, 4, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 2, 3, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 4, 2, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 2, 4, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3, 5], [1, 1, 1, 0]]} "Class ", 2581, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 2, 3, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 2, 3, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 295, 1603, 9893, 68235, 519786, 4332820, 39228356, 383343503, 4021486730, 45076317247, 537621191820, 6798035486701, 90836344796431, 1278924276577978, 18923683675419203] "" "Class ", 2582, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 295, 1601, 9847, 67512, 509749, 4199443, 37468337, 359839643, 3700507483, 40566487194, 472196798843, 5816041850875, 75569869105405, 1032987979331488, 14818189021809246] "" "Class ", 2583, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {3, 4}, {}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {}], [[1, 4, 5, 3, 2], {3}, {}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3, 4}, {}], [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[2, 4, 5, 3, 1], {3}, {}], [[2, 5, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 295, 1600, 9818, 66903, 499463, 4042889, 35201397, 327634122, 3243104529, 33995969933, 376025195932, 4374922955601, 53394681488131, 681940705624063, 9094435155181943] "" "Class ", 2584, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]} "Class ", 2585, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 2, 4, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 2, 3, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 4, 2, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 2, 4, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3, 5], [0, 0, 1, 1]]} "Class ", 2586, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 2, 4, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 4, 2, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 2, 4, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 1, 1]]} "Class ", 2587, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 2, 4, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 4, 2, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 2, 4, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 1, 1]]} "Class ", 2588, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 2, 4, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 2, 3, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 2, 4, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3, 5], [1, 1, 1, 1]]} "Class ", 2589, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 2, 5, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 4, 3, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 4, 1, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 2, 5, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 4, 3, 5], [1, 0, 1, 0]]} "Class ", 2590, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 2, 5, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 4, 1, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 2, 5, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 1, 0]]} "Class ", 2591, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 2, 5, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 4, 3, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 2, 3, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 4, 1, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 2, 5, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 4, 3, 5], [1, 1, 1, 0]]} "Class ", 2592, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 4, 3, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 4, 3, 5], [1, 0, 0, 1]]} "Class ", 2593, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]} "Class ", 2594, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 4, 3, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 4, 3, 5], [1, 1, 0, 1]]} "Class ", 2595, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 2, 5, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 4, 3, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 4, 1, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 2, 5, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 4, 3, 5], [1, 0, 1, 1]]} "Class ", 2596, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 2, 5, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 4, 1, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 2, 5, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 1, 1]]} "Class ", 2597, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 2, 5, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 4, 3, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 2, 3, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 4, 1, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 2, 5, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 4, 3, 5], [1, 1, 1, 1]]} "Class ", 2598, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3, 5], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 4, 3, 1], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 4, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3, 5], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 4, 3, 1], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 4, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {1, 2, 3}, {}], [[1, 4, 5, 2, 3], {1, 2, 3}, {}], [[1, 4, 5, 3, 2], {1, 2, 3, 4}, {}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 287, 1545, 9510, 65869, 507024, 4293103, 39655436, 396816371, 4276200555, 49372906626, 608062320181, 7956765137388, 110242402374791, 1612285439572115, 24820561117577292] "" "Class ", 2599, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3, 5], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 4, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3, 5], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 4, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 283, 1486, 8816, 58262, 424165, 3371685, 29049544, 269612218, 2681420366, 28447081686, 320646488764, 3826504827267, 48195365745658, 638878823079222, 8890911749086377] "" "Class ", 2600, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3, 5], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 4, 3, 1], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 4, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3, 5], [0, 1, 0, 0]]} "Class ", 2601, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3, 5], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 4, 3, 1], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 4, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3, 5], [1, 1, 0, 0]]} "Class ", 2602, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3, 5], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 4, 3, 1], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 4, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3, 5], [0, 0, 1, 0]]} "Class ", 2603, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 4, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3, 5], [1, 0, 1, 0]]} "Class ", 2604, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 4, 3, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 4, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3, 5], [0, 1, 1, 0]]} "Class ", 2605, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 4, 3, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 4, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3, 5], [1, 1, 1, 0]]} "Class ", 2606, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 4, 3, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 4, 3, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 286, 1529, 9309, 63581, 481408, 4001612, 36228222, 354843002, 3738621539, 42162048836, 506744675893, 6466355018848, 87310201054026, 1243639856450730, 18636758926308175] "" "Class ", 2607, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 282, 1467, 8551, 54983, 385369, 2916922, 23667832, 204624659, 1875612331, 18149635561, 184734231769, 1971534311184, 22000389909700, 256068434693763, 3101900006792110] "" "Class ", 2608, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 4, 3, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3, 5], [0, 1, 0, 1]]} "Class ", 2609, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 4, 3, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3, 5], [1, 1, 0, 1]]} "Class ", 2610, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 4, 3, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 4, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3, 5], [0, 0, 1, 1]]} "Class ", 2611, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 4, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3, 5], [1, 0, 1, 1]]} "Class ", 2612, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 4, 3, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 4, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3, 5], [0, 1, 1, 1]]} "Class ", 2613, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 4, 3, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 4, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 4, 2, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3, 5], [1, 1, 1, 1]]} "Class ", 2614, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3, 5], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 3, 1], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3, 5], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 3, 1], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 2, 3, 4, 5], {1}, {}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4}, {}], [[1, 3, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 5, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1512, 9184, 62762, 476728, 3983994, 36325856, 358833636, 3817318736, 43509734688, 528981987072, 6833183820540, 93460549595168, 1349318382203820, 20505810372480384] "" "Class ", 2615, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {[0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 281, 1463, 8600, 56358, 407726, 3228498, 27780766, 258185767, 2577653147, 27515937547, 312763320389, 3771590295893, 48093947311311, 646605910615198, 9141636107002635] "" "Class ", 2616, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3, 5], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 3, 1], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3, 5], [0, 1, 0, 0]]} "Class ", 2617, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3, 5], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 3, 1], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3, 5], [1, 1, 0, 0]]} "Class ", 2618, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3, 5], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 3, 1], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 1, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3, 5], [0, 0, 1, 0]]} "Class ", 2619, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 1, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 1, 0]]} "Class ", 2620, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 3, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 1, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3, 5], [0, 1, 1, 0]]} "Class ", 2621, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 3, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 1, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3, 5], [1, 1, 1, 0]]} "Class ", 2622, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 3, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 3, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 2, 3, 4, 5], {2}, {}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {2}, {}], [[1, 3, 4, 2, 5], {2, 3}, {}], [[1, 3, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {2, 3}, {}], [[1, 4, 5, 2, 3], {2, 3}, {}], [[1, 4, 5, 3, 2], {4}, {}], [[2, 3, 4, 5, 1], {1, 2, 3, 4}, {}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 283, 1491, 8898, 59353, 437580, 3533337, 31014350, 294033029, 2994358207, 32599737075, 377845565004, 4645211851440, 60376120800103, 827219937061205, 11915916124321438] "" "Class ", 2623, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {[0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {}], [[1, 3, 5, 2, 4], {2, 3}, {}], [[1, 4, 5, 2, 3], {2, 3}, {}], [[1, 4, 5, 3, 2], {4}, {}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 281, 1457, 8468, 54389, 381822, 2903811, 23755808, 207821255, 1934454764, 19077247314, 198583916351, 2174847034654, 24987241894095, 300399333918260, 3770268457272633] "" "Class ", 2624, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 3, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3, 5], [0, 1, 0, 1]]} "Class ", 2625, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 3, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3, 5], [1, 1, 0, 1]]} "Class ", 2626, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 3, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 1, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3, 5], [0, 0, 1, 1]]} "Class ", 2627, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 1, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 1, 1]]} "Class ", 2628, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 3, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 1, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3, 5], [0, 1, 1, 1]]} "Class ", 2629, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 3, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 2, 1, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 4, 5, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3, 5], [1, 1, 1, 1]]} "Class ", 2630, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3, 5], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 5, 3, 1], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 1, 4, 2], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3, 5], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 5, 3, 1], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 1, 4, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {1, 2, 3}, {}], [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {}], [[1, 4, 5, 3, 2], {1, 2, 3, 4}, {}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 286, 1533, 9386, 64642, 494702, 4164617, 38247348, 380530806, 4077208334, 46805719022, 573143832904, 7456881767754, 102724606738688, 1493732458835136, 22863754399392066] "" "Class ", 2631, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3, 5], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 5, 3, 1], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 1, 4, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3, 5], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 5, 3, 1], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 1, 4, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 283, 1486, 8816, 58262, 424165, 3371685, 29049544, 269612218, 2681420366, 28447081686, 320646488764, 3826504827267, 48195365745658, 638878823079222, 8890911749086377] "" "Class ", 2632, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3, 5], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 5, 3, 1], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 1, 4, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3, 5], [0, 1, 0, 0]]} "Class ", 2633, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3, 5], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 5, 3, 1], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 1, 4, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3, 5], [1, 1, 0, 0]]} "Class ", 2634, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3, 5], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 5, 3, 1], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 1, 4, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3, 5], [0, 0, 1, 0]]} "Class ", 2635, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 5, 3, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 1, 4, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3, 5], [1, 0, 1, 0]]} "Class ", 2636, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 5, 3, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 1, 4, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3, 5], [0, 1, 1, 0]]} "Class ", 2637, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 5, 3, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 1, 4, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3, 5], [1, 1, 1, 0]]} "Class ", 2638, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 5, 3, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 5, 3, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 285, 1517, 9181, 62250, 467385, 3849348, 34504836, 334418505, 3484725246, 38850176907, 461433206642, 5816762416758, 77563787633431, 1090798658342013, 16135098666190280] "" "Class ", 2639, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 5, 3, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 5, 3, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {[0, 0, 0, 1, 0, 0]}], [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 282, 1467, 8551, 54983, 385369, 2916922, 23667832, 204624659, 1875612331, 18149635561, 184734231769, 1971534311184, 22000389909700, 256068434693763, 3101900006792110] "" "Class ", 2640, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 5, 3, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3, 5], [0, 1, 0, 1]]} "Class ", 2641, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 5, 3, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3, 5], [1, 1, 0, 1]]} "Class ", 2642, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 5, 3, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 1, 4, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3, 5], [0, 0, 1, 1]]} "Class ", 2643, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 5, 3, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 1, 4, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3, 5], [1, 0, 1, 1]]} "Class ", 2644, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 5, 3, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 1, 4, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3, 5], [0, 1, 1, 1]]} "Class ", 2645, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 5, 3, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 1, 4, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 5, 2, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3, 5], [1, 1, 1, 1]]} "Class ", 2646, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 5, 4, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3, 5], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 5, 3, 1], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 1, 2, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 5, 4, 2], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3, 5], [0, 1, 0, 0]]} "Class ", 2647, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 5, 4, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3, 5], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 5, 3, 1], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 1, 2, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 5, 4, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3, 5], [1, 1, 0, 0]]} "Class ", 2648, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 5, 4, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3, 5], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 5, 3, 1], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 1, 2, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 5, 4, 2], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3, 5], [0, 0, 1, 0]]} "Class ", 2649, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 5, 4, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 1, 2, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 5, 4, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3, 5], [1, 0, 1, 0]]} "Class ", 2650, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 5, 4, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 5, 3, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 1, 2, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 5, 4, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3, 5], [0, 1, 1, 0]]} "Class ", 2651, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 5, 4, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 5, 3, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 1, 2, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 5, 4, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3, 5], [1, 1, 1, 0]]} "Class ", 2652, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 5, 3, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3, 5], [0, 1, 0, 1]]} "Class ", 2653, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 5, 3, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3, 5], [1, 1, 0, 1]]} "Class ", 2654, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 5, 4, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 5, 3, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 1, 2, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 5, 4, 2], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3, 5], [0, 0, 1, 1]]} "Class ", 2655, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 5, 4, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 1, 2, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 5, 4, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3, 5], [1, 0, 1, 1]]} "Class ", 2656, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 5, 4, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 5, 3, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 1, 2, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 5, 4, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3, 5], [0, 1, 1, 1]]} "Class ", 2657, " is:" {{[[1, 3, 2], [0, 0]], [[1, 3, 5, 4, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 5, 3, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 3, 1, 2, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 3, 5, 4, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3, 5], [1, 1, 1, 1]]} "Class ", 2658, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 2, 3, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2, 5], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 2, 4, 1], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 4, 3, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 2, 3, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2, 5], [0, 0, 1, 0]]} "Class ", 2659, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 2, 3, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 4, 3, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 2, 3, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 1, 0]]} "Class ", 2660, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 2, 3, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 2, 4, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 4, 3, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 2, 3, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2, 5], [0, 1, 1, 0]]} "Class ", 2661, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 2, 3, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 2, 4, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 4, 3, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 2, 3, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2, 5], [1, 1, 1, 0]]} "Class ", 2662, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 2, 3, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 2, 4, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 2, 3, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 4, 2, 3, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 2, 4, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 294, 1594, 9822, 67790, 517935, 4339440, 39562648, 389919016, 4131037260, 46819083277, 565218383290, 7241187926100, 98119859305630, 1402053727670145, 21070287654728529] "" "Class ", 2663, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 2, 3, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 2, 3, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 4, 2, 3, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 294, 1587, 9685, 65763, 490822, 3988539, 35023093, 330234721, 3326048501, 35621824366, 404104704138, 4839304136934, 60992729031020, 806897230379990, 11177972683498285] "" "Class ", 2664, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 2, 3, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 2, 4, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 2, 3, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2, 5], [0, 1, 0, 1]]} "Class ", 2665, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 2, 3, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 2, 4, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 2, 3, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2, 5], [1, 1, 0, 1]]} "Class ", 2666, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 2, 3, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 2, 4, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 4, 3, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 2, 3, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2, 5], [0, 0, 1, 1]]} "Class ", 2667, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 2, 3, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 4, 3, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 2, 3, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 1, 1]]} "Class ", 2668, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 2, 3, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 2, 4, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 4, 3, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 2, 3, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2, 5], [0, 1, 1, 1]]} "Class ", 2669, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 2, 3, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 2, 4, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 4, 3, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 2, 3, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2, 5], [1, 1, 1, 1]]} "Class ", 2670, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 2, 5, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 4, 2, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 4, 1, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 2, 5, 3], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 1, 4, 2, 5], [1, 0, 1, 0]]} "Class ", 2671, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 2, 5, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 4, 2, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 2, 4, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 4, 1, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 2, 5, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 1, 4, 2, 5], [0, 1, 1, 0]]} "Class ", 2672, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 2, 5, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 4, 2, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 2, 4, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 4, 1, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 2, 5, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 1, 4, 2, 5], [1, 1, 1, 0]]} "Class ", 2673, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 4, 2, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 1, 4, 2, 5], [1, 0, 0, 1]]} "Class ", 2674, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 4, 2, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 2, 4, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 1, 4, 2, 5], [0, 1, 0, 1]]} "Class ", 2675, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 4, 2, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 2, 4, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 1, 4, 2, 5], [1, 1, 0, 1]]} "Class ", 2676, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 2, 5, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 4, 2, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 4, 1, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 2, 5, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 1, 4, 2, 5], [1, 0, 1, 1]]} "Class ", 2677, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 2, 5, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 4, 2, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 2, 4, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 4, 1, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 2, 5, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 1, 4, 2, 5], [0, 1, 1, 1]]} "Class ", 2678, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 2, 5, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 4, 2, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 2, 4, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 4, 1, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 2, 5, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 1, 4, 2, 5], [1, 1, 1, 1]]} "Class ", 2679, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 3, 2, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2, 5], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 3, 4, 1], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 3, 4, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 3, 2, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2, 5], [0, 0, 1, 0]]} "Class ", 2680, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 3, 2, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 3, 4, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 3, 2, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 1, 0]]} "Class ", 2681, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 3, 2, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 3, 4, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 3, 4, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 3, 2, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2, 5], [0, 1, 1, 0]]} "Class ", 2682, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 3, 2, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 3, 4, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 3, 4, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 3, 2, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2, 5], [1, 1, 1, 0]]} "Class ", 2683, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 3, 4, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 3, 4, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 295, 1608, 9998, 69818, 541029, 4606609, 42749466, 429447729, 4642935316, 53752237961, 663467288556, 8697362269022, 120674827969046, 1766778986171089, 27220399706216587] "" "Class ", 2684, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 295, 1604, 9913, 68505, 522910, 4365801, 39555885, 386404910, 4047310144, 45241141750, 537482741580, 6762348113904, 89815256319493, 1255708851902107, 18433439634185050] "" "Class ", 2685, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 3, 4, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2, 5], [0, 1, 0, 1]]} "Class ", 2686, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 3, 4, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2, 5], [1, 1, 0, 1]]} "Class ", 2687, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 3, 2, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 3, 4, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 3, 4, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 3, 2, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2, 5], [0, 0, 1, 1]]} "Class ", 2688, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 3, 2, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 3, 4, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 3, 2, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 1, 1]]} "Class ", 2689, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 3, 2, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 3, 4, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 3, 4, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 3, 2, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2, 5], [0, 1, 1, 1]]} "Class ", 2690, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 3, 2, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 3, 4, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 3, 4, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 3, 2, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2, 5], [1, 1, 1, 1]]} "Class ", 2691, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 3, 5, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2, 5], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 3, 4, 1], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 3, 1, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 3, 5, 2], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2, 5], [0, 0, 1, 0]]} "Class ", 2692, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 3, 5, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 3, 1, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 3, 5, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2, 5], [1, 0, 1, 0]]} "Class ", 2693, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 3, 5, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 3, 4, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 3, 1, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 3, 5, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2, 5], [0, 1, 1, 0]]} "Class ", 2694, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 3, 5, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 3, 4, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 3, 1, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 3, 5, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2, 5], [1, 1, 1, 0]]} "Class ", 2695, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 3, 4, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 3, 4, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {}], [[4, 1, 2, 3], {1, 2, 3}, {}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 295, 1604, 9927, 68880, 529654, 4470732, 41096598, 408665377, 4370979165, 50036953608, 610421313141, 7905770066927, 108335128565913, 1566016658128395, 23814929686702847] "" "Class ", 2696, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2, 5], [1, 0, 0, 1]]} "Class ", 2697, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 3, 4, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2, 5], [0, 1, 0, 1]]} "Class ", 2698, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 3, 4, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2, 5], [1, 1, 0, 1]]} "Class ", 2699, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 3, 5, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 3, 4, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 3, 1, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 3, 5, 2], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2, 5], [0, 0, 1, 1]]} "Class ", 2700, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 3, 5, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 3, 1, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 3, 5, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2, 5], [1, 0, 1, 1]]} "Class ", 2701, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 3, 5, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 3, 4, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 3, 1, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 3, 5, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2, 5], [0, 1, 1, 1]]} "Class ", 2702, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 3, 5, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 3, 4, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 3, 1, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 3, 5, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2, 5], [1, 1, 1, 1]]} "Class ", 2703, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 2, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 5, 4, 1], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 4, 3], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 5, 2, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 2, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 5, 4, 1], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 4, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[1, 4, 5, 2, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {1, 2, 3}, {}], [[1, 3, 5, 2, 4], {1, 2, 3}, {}], [[1, 4, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 3, 2], {1, 2, 3, 4}, {}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 285, 1522, 9275, 63577, 484226, 4057149, 37085035, 367235982, 3916324660, 44748198629, 545382303910, 7062448770880, 96835162659290, 1401496212402804, 21351439327549338] "" "Class ", 2704, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 2, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2, 5], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 5, 4, 1], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 4, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 5, 2, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 2, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2, 5], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 5, 4, 1], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 4, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[1, 4, 5, 2, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 0, 1, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 283, 1486, 8816, 58262, 424165, 3371685, 29049544, 269612218, 2681420366, 28447081686, 320646488764, 3826504827267, 48195365745658, 638878823079222, 8890911749086377] "" "Class ", 2705, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 2, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2, 5], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 5, 4, 1], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 4, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 5, 2, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2, 5], [0, 1, 0, 0]]} "Class ", 2706, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 2, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2, 5], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 5, 4, 1], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 4, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 5, 2, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2, 5], [1, 1, 0, 0]]} "Class ", 2707, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 2, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2, 5], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 5, 4, 1], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 4, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 5, 2, 3], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2, 5], [0, 0, 1, 0]]} "Class ", 2708, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 2, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 5, 4, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 4, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 5, 2, 3], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2, 5], [1, 0, 1, 0]]} "Class ", 2709, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 2, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 5, 4, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 4, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 5, 2, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2, 5], [0, 1, 1, 0]]} "Class ", 2710, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 2, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 5, 4, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 4, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 5, 2, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2, 5], [1, 1, 1, 0]]} "Class ", 2711, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 5, 4, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 5, 4, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 283, 1492, 8919, 59651, 441342, 3579124, 31572296, 300976834, 3083493606, 33786253828, 394266948336, 4881768338696, 63923866522032, 882597358870587, 12815023231802550] "" "Class ", 2712, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 5, 4, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2, 5], [1, 0, 0, 1]]} "Class ", 2713, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 5, 4, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2, 5], [0, 1, 0, 1]]} "Class ", 2714, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 5, 4, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2, 5], [1, 1, 0, 1]]} "Class ", 2715, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 2, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 5, 4, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 4, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 5, 2, 3], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2, 5], [0, 0, 1, 1]]} "Class ", 2716, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 2, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 5, 4, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 4, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 5, 2, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2, 5], [1, 0, 1, 1]]} "Class ", 2717, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 2, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 5, 4, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 4, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 5, 2, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2, 5], [0, 1, 1, 1]]} "Class ", 2718, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 2, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 5, 4, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 4, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 5, 2, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2, 5], [1, 1, 1, 1]]} "Class ", 2719, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2, 5], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 5, 4, 1], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 3, 4], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2, 5], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 5, 4, 1], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 3, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {1, 2, 3}, {}], [[1, 3, 5, 2, 4], {1, 2, 3}, {}], [[1, 4, 5, 2, 3], {1, 2, 3}, {}], [[1, 4, 5, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1512, 9184, 62762, 476728, 3983994, 36325856, 358833636, 3817318736, 43509734688, 528981987072, 6833183820540, 93460549595168, 1349318382203820, 20505810372480384] "" "Class ", 2720, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2, 5], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 5, 4, 1], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 3, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2, 5], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 5, 4, 1], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 3, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 280, 1447, 8416, 54370, 386450, 2997852, 25207084, 228406757, 2219055127, 23012124926, 253721996551, 2963769638202, 36563527877521, 475051467055622, 6483565603799604] "" "Class ", 2721, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2, 5], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 5, 4, 1], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 3, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2, 5], [0, 1, 0, 0]]} "Class ", 2722, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2, 5], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 5, 4, 1], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 3, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2, 5], [1, 1, 0, 0]]} "Class ", 2723, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2, 5], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 5, 4, 1], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 3, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2, 5], [0, 0, 1, 0]]} "Class ", 2724, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 5, 4, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 3, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2, 5], [1, 0, 1, 0]]} "Class ", 2725, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 5, 4, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 3, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2, 5], [0, 1, 1, 0]]} "Class ", 2726, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 5, 4, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 3, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2, 5], [1, 1, 1, 0]]} "Class ", 2727, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 5, 4, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 5, 4, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 282, 1478, 8764, 58020, 424316, 3396916, 29549144, 277536216, 2799217416, 30175069704, 346222937824, 4212800538560, 54185328375344, 734553555025280, 10467850927888672] "" "Class ", 2728, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 5, 4, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 5, 4, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 278, 1408, 7912, 48639, 323726, 2313771, 17640592, 142681797, 1218678524, 10948964653, 103122539696, 1015206288131, 10419655582692, 111238936481903, 1232757715352112] "" "Class ", 2729, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 5, 4, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2, 5], [0, 1, 0, 1]]} "Class ", 2730, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 5, 4, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2, 5], [1, 1, 0, 1]]} "Class ", 2731, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 5, 4, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 3, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2, 5], [0, 0, 1, 1]]} "Class ", 2732, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 5, 4, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 3, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2, 5], [1, 0, 1, 1]]} "Class ", 2733, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 5, 4, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 3, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2, 5], [0, 1, 1, 1]]} "Class ", 2734, " is:" {{[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 5, 4, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 2, 1, 3, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 4, 5, 3, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2, 5], [1, 1, 1, 1]]} "Class ", 2735, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 2, 3, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1, 5], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 2, 5, 1], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 4, 3, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 2, 3, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1, 5], [0, 0, 1, 0]]} "Class ", 2736, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 2, 3, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 4, 3, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 2, 3, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1, 5], [1, 0, 1, 0]]} "Class ", 2737, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 2, 3, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 2, 5, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 4, 3, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 2, 3, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1, 5], [0, 1, 1, 0]]} "Class ", 2738, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 2, 3, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 2, 5, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 4, 3, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 2, 3, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1, 5], [1, 1, 1, 0]]} "Class ", 2739, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 293, 1578, 9631, 65657, 494521, 4077080, 36522481, 353216087, 3667850175, 40702326839, 480684345652, 6019311553714, 79665144197529, 1111122107107645, 16288868360171689] "" "Class ", 2740, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1, 5], [1, 0, 0, 1]]} "Class ", 2741, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 2, 5, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1, 5], [0, 1, 0, 1]]} "Class ", 2742, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 2, 5, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1, 5], [1, 1, 0, 1]]} "Class ", 2743, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 2, 3, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 2, 5, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 4, 3, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 2, 3, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1, 5], [0, 0, 1, 1]]} "Class ", 2744, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 2, 3, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 4, 3, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 2, 3, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1, 5], [1, 0, 1, 1]]} "Class ", 2745, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 2, 3, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 2, 5, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 4, 3, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 2, 3, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1, 5], [0, 1, 1, 1]]} "Class ", 2746, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 2, 3, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 2, 5, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 4, 3, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 2, 3, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1, 5], [1, 1, 1, 1]]} "Class ", 2747, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 2, 4, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 4, 1, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 4, 2, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 2, 4, 3], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 2, 4, 1, 5], [1, 0, 1, 0]]} "Class ", 2748, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 2, 4, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 4, 1, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 2, 5, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 4, 2, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 2, 4, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 2, 4, 1, 5], [0, 1, 1, 0]]} "Class ", 2749, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 2, 4, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 4, 1, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 4, 2, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 2, 4, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 2, 4, 1, 5], [1, 1, 1, 0]]} "Class ", 2750, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 4, 1, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 2, 4, 1, 5], [1, 0, 0, 1]]} "Class ", 2751, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 4, 1, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 2, 5, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 2, 4, 1, 5], [0, 1, 0, 1]]} "Class ", 2752, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 4, 1, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 2, 5, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 2, 4, 1, 5], [1, 1, 0, 1]]} "Class ", 2753, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 2, 4, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 4, 1, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 4, 2, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 2, 4, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 2, 4, 1, 5], [1, 0, 1, 1]]} "Class ", 2754, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 2, 4, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 4, 1, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 2, 5, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 4, 2, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 2, 4, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 2, 4, 1, 5], [0, 1, 1, 1]]} "Class ", 2755, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 2, 4, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 4, 1, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 4, 2, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 2, 4, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 2, 4, 1, 5], [1, 1, 1, 1]]} "Class ", 2756, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 3, 2, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1, 5], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 3, 5, 1], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 3, 4, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 3, 2, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1, 5], [0, 0, 1, 0]]} "Class ", 2757, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 3, 2, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 3, 5, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 3, 4, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 3, 2, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1, 5], [1, 0, 1, 0]]} "Class ", 2758, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 3, 2, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 3, 5, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 3, 4, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 3, 2, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1, 5], [0, 1, 1, 0]]} "Class ", 2759, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 3, 2, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 3, 5, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 3, 4, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 3, 2, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1, 5], [1, 1, 1, 0]]} "Class ", 2760, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 3, 5, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 3, 5, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 294, 1594, 9840, 68102, 522441, 4399359, 40343686, 400230197, 4270675632, 48774305222, 593633678002, 7670537955702, 104869263410282, 1512434323004744, 22947438057296724] "" "Class ", 2761, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 3, 5, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 3, 5, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {}], [[1, 3, 5, 2, 4], {2, 3}, {}], [[1, 4, 5, 2, 3], {2, 3}, {}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 294, 1588, 9719, 66331, 498987, 4098967, 36494234, 349998287, 3596864782, 39431878872, 459340531180, 5666108721650, 73784248209913, 1011521147338252, 14562626953848097] "" "Class ", 2762, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 3, 5, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1, 5], [0, 1, 0, 1]]} "Class ", 2763, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 3, 5, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1, 5], [1, 1, 0, 1]]} "Class ", 2764, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 3, 2, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 3, 5, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 3, 4, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 3, 2, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1, 5], [0, 0, 1, 1]]} "Class ", 2765, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 3, 2, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 3, 5, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 3, 4, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 3, 2, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1, 5], [1, 0, 1, 1]]} "Class ", 2766, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 3, 2, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 3, 5, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 3, 4, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 3, 2, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1, 5], [0, 1, 1, 1]]} "Class ", 2767, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 3, 2, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 3, 5, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 3, 4, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 3, 2, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1, 5], [1, 1, 1, 1]]} "Class ", 2768, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 3, 4, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1, 5], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 3, 5, 1], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 3, 2, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 3, 4, 2], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1, 5], [0, 0, 1, 0]]} "Class ", 2769, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 3, 4, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 3, 2, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 3, 4, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1, 5], [1, 0, 1, 0]]} "Class ", 2770, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 3, 4, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 3, 5, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 3, 2, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 3, 4, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1, 5], [0, 1, 1, 0]]} "Class ", 2771, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 3, 4, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 3, 5, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 3, 2, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 3, 4, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1, 5], [1, 1, 1, 0]]} "Class ", 2772, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 3, 5, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 3, 5, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {}], [[4, 1, 2, 3], {1, 2, 3}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 294, 1589, 9768, 67288, 513433, 4298954, 39187877, 386333335, 4095708853, 46464186389, 561649009652, 7206536783914, 97823979240411, 1400613487117316, 21094750101709097] "" "Class ", 2773, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1, 5], [1, 0, 0, 1]]} "Class ", 2774, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 3, 5, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1, 5], [0, 1, 0, 1]]} "Class ", 2775, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 3, 5, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1, 5], [1, 1, 0, 1]]} "Class ", 2776, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 3, 4, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 3, 5, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 3, 2, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 3, 4, 2], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1, 5], [0, 0, 1, 1]]} "Class ", 2777, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 3, 4, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 3, 2, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 3, 4, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1, 5], [1, 0, 1, 1]]} "Class ", 2778, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 3, 4, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 3, 5, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 3, 2, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 3, 4, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1, 5], [0, 1, 1, 1]]} "Class ", 2779, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 3, 4, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 3, 5, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 3, 2, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 3, 4, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1, 5], [1, 1, 1, 1]]} "Class ", 2780, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 4, 2, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1, 5], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 4, 5, 1], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 2, 4, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 4, 2, 3], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1, 5], [0, 0, 1, 0]]} "Class ", 2781, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 4, 2, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 4, 5, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 2, 4, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 4, 2, 3], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1, 5], [1, 0, 1, 0]]} "Class ", 2782, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 4, 2, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 4, 5, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 2, 4, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 4, 2, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1, 5], [0, 1, 1, 0]]} "Class ", 2783, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 4, 2, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 4, 5, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 2, 4, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 4, 2, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1, 5], [1, 1, 1, 0]]} "Class ", 2784, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 4, 5, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 4, 5, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 295, 1606, 9967, 69427, 536388, 4551994, 42091712, 421237039, 4536064229, 52297751426, 642753664751, 8388752022884, 115867991405859, 1688586997784017, 25893570860628051] "" "Class ", 2785, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 4, 5, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 4, 5, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {}], [[1, 3, 5, 2, 4], {2, 3}, {}], [[1, 4, 5, 2, 3], {2, 3}, {}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 1, 0, 0, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 295, 1604, 9915, 68542, 523414, 4372029, 39629595, 387270206, 4057554339, 45364345611, 538993356515, 6781230874317, 90055199433533, 1258789756139551, 18472978356928327] "" "Class ", 2786, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 4, 5, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1, 5], [0, 1, 0, 1]]} "Class ", 2787, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 4, 5, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1, 5], [1, 1, 0, 1]]} "Class ", 2788, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 4, 2, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 4, 5, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 2, 4, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 4, 2, 3], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1, 5], [0, 0, 1, 1]]} "Class ", 2789, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 4, 2, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 4, 5, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 2, 4, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 4, 2, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1, 5], [1, 0, 1, 1]]} "Class ", 2790, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 4, 2, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 4, 5, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 2, 4, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 4, 2, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1, 5], [0, 1, 1, 1]]} "Class ", 2791, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 4, 2, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 4, 5, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 2, 4, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 4, 2, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1, 5], [1, 1, 1, 1]]} "Class ", 2792, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 4, 3, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1, 5], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 4, 5, 1], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 2, 3, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 4, 3, 2], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1, 5], [0, 0, 1, 0]]} "Class ", 2793, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 4, 3, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 4, 5, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 2, 3, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 4, 3, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1, 5], [1, 0, 1, 0]]} "Class ", 2794, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 4, 3, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 4, 5, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 2, 3, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 4, 3, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1, 5], [0, 1, 1, 0]]} "Class ", 2795, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 4, 3, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 4, 5, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 2, 3, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 4, 3, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1, 5], [1, 1, 1, 0]]} "Class ", 2796, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {}], [[1, 3, 5, 2, 4], {2, 3}, {}], [[1, 4, 5, 2, 3], {2, 3}, {}], [[1, 4, 5, 3, 2], {2, 3, 4}, {}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 295, 1606, 9972, 69539, 538101, 4575518, 42406092, 425464965, 4594292831, 53126219924, 654983220080, 8576444659059, 118865308813169, 1738393271486206, 26754419200157572] "" "Class ", 2797, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {}], [[1, 3, 5, 2, 4], {2, 3}, {}], [[1, 4, 5, 2, 3], {2, 3}, {}], [[1, 4, 5, 3, 2], {1, 2, 3, 4}, {[0, 1, 0, 0, 0, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 295, 1601, 9862, 67895, 516232, 4293837, 38766742, 377449511, 3941365017, 43930191943, 520496255019, 6531889417451, 86543767736722, 1207168846437043, 17681613105682349] "" "Class ", 2798, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 4, 5, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1, 5], [0, 1, 0, 1]]} "Class ", 2799, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 4, 5, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1, 5], [1, 1, 0, 1]]} "Class ", 2800, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 4, 3, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 4, 5, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 4, 3, 2], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]} "Class ", 2801, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 4, 5, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1, 5], [1, 0, 1, 1]]} "Class ", 2802, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 4, 3, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 4, 5, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 2, 3, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 4, 3, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1, 5], [0, 1, 1, 1]]} "Class ", 2803, " is:" {{[[1, 3, 2], [0, 0]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 4, 5, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]} "Class ", 2804, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}], [[2, 1, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3}, {}], [[3, 1, 4, 5, 2], {1, 2, 3}, {}], [[3, 2, 4, 5, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 286, 1533, 9388, 64684, 495324, 4172847, 38352564, 381881613, 4094969176, 47047427058, 576566626280, 7507438032707, 103504071586138, 1506274556565187, 23074230114335796] "" "Class ", 2805, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 283, 1492, 8935, 59920, 444955, 3624109, 32120382, 307734512, 3169037814, 34906946765, 409525211299, 5098061648085, 67118105894909, 931736245230149, 13602033965330403] "" "Class ", 2806, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 2, 3, 4, 5], {3}, {}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {3}, {}], [[1, 2, 5, 3, 4], {3}, {}], [[1, 2, 5, 4, 3], {3}, {}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {3}, {}], [[1, 3, 5, 2, 4], {3, 4}, {}], [[1, 3, 5, 4, 2], {3}, {}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {}], [[1, 4, 5, 3, 2], {3}, {}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 5, 1], {3}, {}], [[2, 3, 5, 1, 4], {3, 4}, {}], [[2, 3, 5, 4, 1], {3}, {}], [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[2, 4, 5, 3, 1], {3}, {}], [[2, 5, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 285, 1510, 9077, 60964, 452352, 3674500, 32428678, 308941208, 3159774907, 34530110418, 401505630769, 4949292430153, 64466802739459, 884718175645393, 12758847219778869] "" "Class ", 2807, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 1, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [1, 1, 0, 0]]} "Class ", 2808, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 1, 0]]} "Class ", 2809, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]} "Class ", 2810, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 1, 0]]} "Class ", 2811, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [1, 1, 1, 0]]} "Class ", 2812, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0]}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 282, 1474, 8700, 57230, 415344, 3297498, 28436224, 264749068, 2647116054, 28292869356, 321937740072, 3885800108480, 49590067445140, 667191113160566, 9438568805706744] "" "Class ", 2813, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0]}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 279, 1420, 8018, 49525, 331269, 2380617, 18264458, 148829745, 1282485289, 11643649330, 111022570697, 1108675448552, 11566356603274, 125786266368289, 1423175074930417] "" "Class ", 2814, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[1, 2, 4, 3], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {3, 4}, {[0, 0, 0, 1, 0, 0]}], [[1, 2, 5, 4, 3], {3}, {}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {3, 4}, {}], [[1, 3, 5, 4, 2], {3}, {}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {}], [[1, 4, 5, 3, 2], {3}, {}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3, 4}, {}], [[2, 3, 5, 4, 1], {3}, {}], [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[2, 4, 5, 3, 1], {3}, {}], [[2, 5, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 281, 1448, 8305, 52182, 355162, 2596063, 20242278, 167453036, 1462966327, 13446428270, 129589348977, 1305780410194, 13721896577018, 150049221475052, 1703993856574850] "" "Class ", 2815, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [1, 1, 0, 1]]} "Class ", 2816, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 3, 2, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 1, 1]]} "Class ", 2817, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 3, 2, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 1, 1]]} "Class ", 2818, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 3, 2, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 1, 1]]} "Class ", 2819, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 3, 2, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3, 4, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 3, 5, 4], [1, 1, 1, 1]]} "Class ", 2820, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 5, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 3, 5, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 3, 1, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3, 5, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 5, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 3, 5, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 3, 1, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 1, 3, 5, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 292, 1565, 9517, 64688, 486227, 4004040, 35846048, 346641387, 3600821089, 39986860802, 472725319463, 5927476342899, 78573110352302, 1097859052690214, 16126530137868189] "" "Class ", 2821, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 5, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3, 5, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 0]]} "Class ", 2822, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 5, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 3, 5, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 3, 1, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3, 5, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 3, 5, 4], [1, 1, 0, 0]]} "Class ", 2823, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 3, 5, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 3, 5, 4], [1, 0, 1, 0]]} "Class ", 2824, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 1, 0]]} "Class ", 2825, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 3, 5, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 3, 1, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 3, 5, 4], [1, 1, 1, 0]]} "Class ", 2826, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 5, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 3, 5, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 3, 1, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 3, 1, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3, 5, 4], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 3, 5, 4], [1, 0, 0, 1]]} "Class ", 2827, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 5, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3, 5, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]} "Class ", 2828, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 5, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 3, 5, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 3, 1, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3, 5, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 3, 5, 4], [1, 1, 0, 1]]} "Class ", 2829, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 5, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 3, 5, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 3, 1, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3, 5, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 3, 5, 4], [1, 0, 1, 1]]} "Class ", 2830, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 5, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 3, 1, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3, 5, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 1, 1]]} "Class ", 2831, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 5, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 3, 5, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 3, 1, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 3, 1, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3, 5, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 3, 5, 4], [1, 1, 1, 1]]} "Class ", 2832, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 4, 3, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 2, 5, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 4, 1, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 4, 3, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 2, 5, 4], [0, 1, 0, 0]]} "Class ", 2833, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 4, 3, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 2, 5, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 4, 1, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 4, 3, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 2, 5, 4], [1, 1, 0, 0]]} "Class ", 2834, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 2, 5, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 2, 5, 4], [0, 0, 1, 0]]} "Class ", 2835, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]} "Class ", 2836, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 2, 5, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 4, 1, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 2, 5, 4], [0, 1, 1, 0]]} "Class ", 2837, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 2, 5, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 4, 1, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 2, 5, 4], [1, 1, 1, 0]]} "Class ", 2838, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 4, 3, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 2, 5, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 4, 1, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 4, 3, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 2, 5, 4], [0, 1, 0, 1]]} "Class ", 2839, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 4, 3, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 2, 5, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 4, 1, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 4, 3, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 2, 5, 4], [1, 1, 0, 1]]} "Class ", 2840, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 4, 3, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 2, 5, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 2, 3, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 4, 3, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 2, 5, 4], [0, 0, 1, 1]]} "Class ", 2841, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 4, 3, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 4, 3, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 1]]} "Class ", 2842, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 4, 3, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 2, 5, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 4, 1, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 2, 3, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 4, 3, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 2, 5, 4], [0, 1, 1, 1]]} "Class ", 2843, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 4, 3, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 2, 5, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 4, 1, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 2, 3, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 4, 3, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 2, 5, 4], [1, 1, 1, 1]]} "Class ", 2844, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 5, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 1, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 5, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 1, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {2, 3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 285, 1525, 9325, 64207, 491558, 4140972, 38060398, 378975235, 4063724214, 46686632031, 572116583182, 7449095377095, 102694155502654, 1494407991738455, 22891237744197742] "" "Class ", 2845, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 5, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 5, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2}, {[0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 282, 1482, 8843, 59093, 437427, 3552399, 31400119, 300083414, 3082976894, 33883245622, 396671708680, 4928047223853, 64754079402247, 897250208687851, 13075255952498071] "" "Class ", 2846, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 5, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 1, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 2, 1, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 1, 2, 5, 4], [0, 1, 0, 0]]} "Class ", 2847, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 5, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 1, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 2, 1, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 1, 2, 5, 4], [1, 1, 0, 0]]} "Class ", 2848, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 5, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 1, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 5, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 1, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 3, 4, 5], {3}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {2, 3, 4}, {}], [[3, 2, 4, 5, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 282, 1477, 8744, 57714, 420152, 3342913, 28853528, 268470546, 2678372216, 28516602003, 322706772376, 3867602263506, 48934415811968, 651760309017429, 9114834595279936] "" "Class ", 2849, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 5, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 5, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {[0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 3, 4, 5], {3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 4}, {[0, 0, 0, 1, 0, 0]}], [[3, 2, 4, 5, 1], {1, 2, 4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 280, 1444, 8348, 53362, 373366, 2835364, 23208928, 203602949, 1904822360, 18924499619, 198924910812, 2205126227009, 25704090890994, 314249078700007, 4020127635088244] "" "Class ", 2850, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 5, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 1, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 1, 2, 5, 4], [0, 1, 1, 0]]} "Class ", 2851, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 5, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 1, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 1, 2, 5, 4], [1, 1, 1, 0]]} "Class ", 2852, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 5, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 1, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 2, 1, 3], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[3, 1, 2, 5, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 5, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 1, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 2, 1, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[3, 1, 2, 5, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {1, 2, 3}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 281, 1459, 8531, 55435, 396291, 3090885, 26119707, 237748140, 2319137904, 24136341161, 266966103503, 3127341273235, 38679715365530, 503698568115024, 6888825812715282] "" "Class ", 2853, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 5, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 2, 1, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 1, 2, 5, 4], [1, 0, 0, 1]]} "Class ", 2854, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 5, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 1, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 2, 1, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 1, 2, 5, 4], [0, 1, 0, 1]]} "Class ", 2855, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 5, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 1, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 2, 1, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 1, 2, 5, 4], [1, 1, 0, 1]]} "Class ", 2856, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 5, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 1, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 2, 1, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[3, 1, 2, 5, 4], [0, 0, 1, 1]]} "Class ", 2857, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 5, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 2, 1, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 1, 2, 5, 4], [1, 0, 1, 1]]} "Class ", 2858, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 5, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 1, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 2, 1, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 1, 2, 5, 4], [0, 1, 1, 1]]} "Class ", 2859, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2, 5, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 4, 1, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 2, 1, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 4, 5, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 1, 2, 5, 4], [1, 1, 1, 1]]} "Class ", 2860, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 5, 3, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1, 5, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 5, 1, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 1, 3, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 5, 3, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 3, 1, 5, 4], [0, 1, 0, 0]]} "Class ", 2861, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 5, 3, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1, 5, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 5, 1, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 1, 3, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 5, 3, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 3, 1, 5, 4], [1, 1, 0, 0]]} "Class ", 2862, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1, 5, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 3, 1, 5, 4], [0, 0, 1, 0]]} "Class ", 2863, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 3, 4, 5], {3}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 1, 4, 5, 2], {2, 3, 4}, {}], [[3, 2, 4, 5, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 294, 1586, 9682, 65841, 493006, 4027232, 35621782, 339067496, 3454838608, 37512136467, 432318406756, 5270054711033, 67743646632346, 915733744821727, 12985023060168002] "" "Class ", 2864, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1, 5, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 5, 1, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 3, 1, 5, 4], [0, 1, 1, 0]]} "Class ", 2865, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1, 5, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 5, 1, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 3, 1, 5, 4], [1, 1, 1, 0]]} "Class ", 2866, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 5, 3, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1, 5, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 5, 1, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 1, 3, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 5, 3, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 3, 1, 5, 4], [0, 1, 0, 1]]} "Class ", 2867, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 5, 3, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1, 5, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 5, 1, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 1, 3, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 5, 3, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 3, 1, 5, 4], [1, 1, 0, 1]]} "Class ", 2868, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 5, 3, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1, 5, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 1, 3, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 5, 3, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 3, 1, 5, 4], [0, 0, 1, 1]]} "Class ", 2869, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 5, 3, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 1, 3, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 5, 3, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 1]]} "Class ", 2870, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 5, 3, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1, 5, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 5, 1, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 1, 3, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 5, 3, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 3, 1, 5, 4], [0, 1, 1, 1]]} "Class ", 2871, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 5, 3, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1, 5, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 5, 1, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 1, 3, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 5, 3, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 3, 1, 5, 4], [1, 1, 1, 1]]} "Class ", 2872, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 5, 4, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 1, 5, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 5, 1, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 1, 2, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 5, 4, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 2, 1, 5, 4], [0, 1, 0, 0]]} "Class ", 2873, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 5, 4, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 1, 5, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 5, 1, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 1, 2, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 5, 4, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 2, 1, 5, 4], [1, 1, 0, 0]]} "Class ", 2874, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 1, 5, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 5, 1, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[3, 2, 1, 5, 4], [0, 0, 1, 0]]} "Class ", 2875, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 1, 5, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 2, 1, 5, 4], [1, 0, 1, 0]]} "Class ", 2876, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 1, 5, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 5, 1, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 2, 1, 5, 4], [0, 1, 1, 0]]} "Class ", 2877, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 1, 5, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 5, 1, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 2, 1, 5, 4], [1, 1, 1, 0]]} "Class ", 2878, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 5, 4, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 1, 5, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 5, 1, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 1, 2, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 5, 4, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 2, 1, 5, 4], [0, 1, 0, 1]]} "Class ", 2879, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 5, 4, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 1, 5, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 5, 1, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 1, 2, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 5, 4, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 2, 1, 5, 4], [1, 1, 0, 1]]} "Class ", 2880, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 5, 4, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 1, 5, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 5, 1, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 1, 2, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 5, 4, 3], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[3, 2, 1, 5, 4], [0, 0, 1, 1]]} "Class ", 2881, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 5, 4, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 1, 5, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 1, 2, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 5, 4, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 2, 1, 5, 4], [1, 0, 1, 1]]} "Class ", 2882, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 5, 4, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 1, 5, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 5, 1, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 1, 2, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 5, 4, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 2, 1, 5, 4], [0, 1, 1, 1]]} "Class ", 2883, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 5, 4, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 1, 5, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 5, 1, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 5, 1, 2, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 5, 4, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 2, 1, 5, 4], [1, 1, 1, 1]]} "Class ", 2884, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 3, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 3, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 285, 1520, 9247, 63237, 480392, 4013984, 36587518, 361283794, 3841912607, 43773296403, 531985256273, 6869400227781, 93920762229620, 1355456192041591, 20591394339992160] "" "Class ", 2885, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1507, 9108, 61778, 464800, 3841776, 34603849, 337356772, 3539236370, 39756493581, 476086479337, 6054422882842, 81486949692363, 1157203770926394, 17292224883328488] "" "Class ", 2886, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 5, 2, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 5, 2, 1], [0, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 4, 3], {3}, {}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {3, 4}, {}], [[1, 3, 5, 4, 2], {3}, {}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {}], [[1, 4, 5, 3, 2], {3}, {}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3, 4}, {}], [[2, 3, 5, 4, 1], {3}, {}], [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[2, 4, 5, 3, 1], {3}, {}], [[2, 5, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 282, 1472, 8660, 56660, 407920, 3203612, 27248088, 249465680, 2445644120, 25557440840, 283572178000, 3329010378128, 41221490907168, 536886973250000, 7336801790626880] "" "Class ", 2887, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 3, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 5, 2, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [1, 1, 0, 0]]} "Class ", 2888, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 3, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 5, 2, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [0, 0, 1, 0]]} "Class ", 2889, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 5, 2, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 1, 0]]} "Class ", 2890, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 5, 2, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 1, 0]]} "Class ", 2891, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 3, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 5, 2, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [1, 1, 1, 0]]} "Class ", 2892, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 285, 1514, 9135, 61682, 460683, 3770525, 33559270, 322712263, 3334289381, 36837327507, 433353433786, 5408213010502, 71365865440748, 992822722026035, 14522631622575145] "" "Class ", 2893, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {[0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1501, 8990, 60102, 443313, 3574808, 31277346, 295050959, 2984845642, 32231578803, 370005916582, 4499324564310, 57771757366056, 781048705748805, 11089813459418234] "" "Class ", 2894, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {}, {[0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 4, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {3, 4}, {}], [[1, 3, 5, 4, 2], {3}, {[0, 0, 0, 0, 1, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {}], [[1, 4, 5, 3, 2], {3}, {}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3, 4}, {}], [[2, 3, 5, 4, 1], {3}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[2, 4, 5, 3, 1], {3}, {}], [[2, 5, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 282, 1467, 8553, 55058, 386953, 2943672, 24074187, 210486960, 1958324725, 19310847613, 201129955582, 2205955638325, 25409557739081, 306646115802042, 3868846734814076] "" "Class ", 2895, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [1, 1, 0, 1]]} "Class ", 2896, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 3, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 5, 2, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [0, 0, 1, 1]]} "Class ", 2897, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 5, 2, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 1, 1]]} "Class ", 2898, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 5, 2, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 1, 1]]} "Class ", 2899, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 3, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 5, 2, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1, 4, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 5, 3, 4], [1, 1, 1, 1]]} "Class ", 2900, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 5, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 5, 3, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 1, 3, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1, 5, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 5, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 5, 3, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 1, 3, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 3, 1, 5, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 294, 1591, 9797, 67587, 516351, 4327793, 39481965, 389463945, 4130656802, 46873379169, 566670056793, 7271016335240, 98688854655152, 1412702848784961, 21270421992712830] "" "Class ", 2901, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 5, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1, 5, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 0]]} "Class ", 2902, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 5, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 5, 3, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 1, 3, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1, 5, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 5, 3, 4], [1, 1, 0, 0]]} "Class ", 2903, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 5, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 5, 3, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 1, 3, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 5, 1, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1, 5, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 5, 3, 4], [1, 0, 1, 0]]} "Class ", 2904, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 5, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 5, 1, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1, 5, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 1, 0]]} "Class ", 2905, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 5, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 5, 3, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 1, 3, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 5, 1, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1, 5, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 5, 3, 4], [1, 1, 1, 0]]} "Class ", 2906, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 5, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 5, 3, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 1, 3, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1, 5, 4], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 5, 3, 4], [1, 0, 0, 1]]} "Class ", 2907, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]} "Class ", 2908, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 5, 3, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 1, 3, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 5, 3, 4], [1, 1, 0, 1]]} "Class ", 2909, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 5, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 5, 3, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 1, 3, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 5, 1, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1, 5, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 5, 3, 4], [1, 0, 1, 1]]} "Class ", 2910, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 5, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 5, 1, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1, 5, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 1, 1]]} "Class ", 2911, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 5, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 5, 3, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 1, 3, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 5, 1, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1, 5, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 5, 3, 4], [1, 1, 1, 1]]} "Class ", 2912, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 3, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 3, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 4, 1, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 3, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 3, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 3, 4, 1, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {}, {}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {1, 2, 3}, {}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 288, 1562, 9685, 67590, 524090, 4469957, 41588726, 419184704, 4550106519, 52917743287, 656462682290, 8652621940488, 120756061171330, 1778898758164233, 27584804601278518] "" "Class ", 2913, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 4, 1, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 3, 4, 1, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1506, 9060, 60956, 453256, 3690618, 32659736, 312094777, 3202848290, 35130559236, 410127162654, 5077380315708, 66439980004290, 916262342855698, 13282187703082900] "" "Class ", 2914, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 1, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 3, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 3, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 5, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 4, 1, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 2, 3, 4], [0, 1, 0, 0]]} "Class ", 2915, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 1, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 3, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 3, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 5, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 4, 1, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 2, 3, 4], [1, 1, 0, 0]]} "Class ", 2916, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 1, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 3, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 3, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 5, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 4, 1, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 2, 3, 4], [0, 0, 1, 0]]} "Class ", 2917, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 1, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 5, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 4, 1, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 1, 0]]} "Class ", 2918, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 1, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 3, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 3, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 5, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 4, 1, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 2, 3, 4], [0, 1, 1, 0]]} "Class ", 2919, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 1, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 3, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 3, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 5, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 4, 1, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 2, 3, 4], [1, 1, 1, 0]]} "Class ", 2920, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 1, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 3, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 3, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 4, 1, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 2, 3, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 1, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 3, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 3, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 5, 2, 3, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 287, 1542, 9446, 64935, 494905, 4140703, 37726779, 371808286, 3940821152, 44699171122, 540232207548, 6930718219567, 94065105400512, 1346555587192540, 20276424622228414] "" "Class ", 2921, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 1, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 4, 1, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 1, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 283, 1481, 8700, 56452, 399672, 3058506, 25110729, 219849221, 2042285190, 20043696985, 207068178269, 2244579598167, 25457968929662, 301369926829162, 3715353369569184] "" "Class ", 2922, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 1, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 3, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 3, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 4, 1, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 2, 3, 4], [0, 1, 0, 1]]} "Class ", 2923, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 1, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 3, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 3, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 4, 1, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 2, 3, 4], [1, 1, 0, 1]]} "Class ", 2924, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 1, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 3, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 3, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 5, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 4, 1, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 2, 3, 4], [0, 0, 1, 1]]} "Class ", 2925, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 1, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 5, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 4, 1, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 1, 1]]} "Class ", 2926, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 1, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 3, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 3, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 5, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 4, 1, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 2, 3, 4], [0, 1, 1, 1]]} "Class ", 2927, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 1, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 3, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 3, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 5, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 4, 1, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 2, 3, 4], [1, 1, 1, 1]]} "Class ", 2928, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 2, 3, 4, 5], {1}, {}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4}, {}], [[1, 3, 4, 5, 2], {1, 2, 3, 4}, {}], [[2, 3, 4, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1520, 9312, 64218, 492408, 4153130, 38206944, 380771716, 4086627792, 46992285200, 576396811008, 7511840631612, 103655973202464, 1509814376833260, 23148828107861376] "" "Class ", 2929, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {[1, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 282, 1482, 8834, 58878, 434010, 3504592, 30760170, 291569974, 2968023070, 32290622540, 373896461366, 4590775303510, 59574143906570, 814695306568412, 11709943512555850] "" "Class ", 2930, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 5, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 3, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 3, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 1, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 4, 5, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 2, 3, 4], [0, 1, 0, 0]]} "Class ", 2931, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 5, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 3, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 4, 5, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]} "Class ", 2932, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 5, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 3, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 3, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 1, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 4, 5, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 2, 3, 4], [0, 0, 1, 0]]} "Class ", 2933, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 5, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 1, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 4, 5, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 1, 0]]} "Class ", 2934, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 5, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 3, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 3, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 1, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 4, 5, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 2, 3, 4], [0, 1, 1, 0]]} "Class ", 2935, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 5, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 3, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 3, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 1, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 4, 5, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 2, 3, 4], [1, 1, 1, 0]]} "Class ", 2936, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 283, 1496, 8968, 60126, 445846, 3621017, 31970266, 304863492, 3122397228, 34184418857, 398381777655, 4923801363726, 64329333950639, 885832070661868, 12822827646347300] "" "Class ", 2937, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2, 3}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {2}, {}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 281, 1457, 8468, 54389, 381822, 2903811, 23755808, 207821255, 1934454764, 19077247314, 198583916351, 2174847034654, 24987241894095, 300399333918260, 3770268457272633] "" "Class ", 2938, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 5, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 3, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 3, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 1, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 4, 5, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 2, 3, 4], [0, 1, 0, 1]]} "Class ", 2939, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 5, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 1, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 4, 5, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]} "Class ", 2940, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 5, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 3, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 3, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 1, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 4, 5, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 2, 3, 4], [0, 0, 1, 1]]} "Class ", 2941, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 5, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 1, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 4, 5, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 1, 1]]} "Class ", 2942, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 5, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 3, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 3, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 1, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 4, 5, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 2, 3, 4], [0, 1, 1, 1]]} "Class ", 2943, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 5, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 4, 5, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]} "Class ", 2944, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 5, 1, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 1, 3, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 5, 3, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 1, 5, 2], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 5, 1, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 3, 5, 1, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 1, 3, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 5, 3, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 1, 5, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 3, 5, 1, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {}, {}], [[2, 3, 4, 1, 5], {1, 2, 3}, {}], [[2, 3, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 287, 1550, 9564, 66410, 512333, 4347678, 40248632, 403648029, 4359544952, 50447848863, 622691508344, 8166430060896, 113400524967429, 1662183621417615, 25645981365345450] "" "Class ", 2945, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 5, 1, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 1, 3, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 5, 3, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 1, 5, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 5, 1, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 3, 5, 1, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 1, 3, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 5, 3, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 1, 5, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 3, 5, 1, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1506, 9060, 60956, 453256, 3690618, 32659736, 312094777, 3202848290, 35130559236, 410127162654, 5077380315708, 66439980004290, 916262342855698, 13282187703082900] "" "Class ", 2946, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 5, 1, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 1, 3, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 5, 3, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 1, 5, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 5, 1, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 1, 3, 4], [0, 1, 0, 0]]} "Class ", 2947, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 5, 1, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 1, 3, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 5, 3, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 1, 5, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 5, 1, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 1, 3, 4], [1, 1, 0, 0]]} "Class ", 2948, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 5, 1, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 1, 3, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 5, 3, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 1, 5, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 5, 1, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 1, 3, 4], [0, 0, 1, 0]]} "Class ", 2949, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 5, 1, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 1, 3, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 5, 3, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 1, 5, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 5, 1, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 1, 3, 4], [1, 0, 1, 0]]} "Class ", 2950, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 5, 1, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 1, 3, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 5, 3, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 1, 5, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 5, 1, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 1, 3, 4], [0, 1, 1, 0]]} "Class ", 2951, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 5, 1, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 1, 3, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 5, 3, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 1, 5, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 5, 1, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 1, 3, 4], [1, 1, 1, 0]]} "Class ", 2952, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 5, 1, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 1, 3, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 5, 3, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 1, 5, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 5, 1, 4], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 1, 3, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 3, 5, 1, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 1, 3, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 5, 3, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 1, 5, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[2, 5, 1, 3, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 286, 1529, 9303, 63426, 478855, 3965268, 35732425, 348100470, 3645410113, 40838118410, 487313714191, 6170808384099, 82645036634286, 1167180538719308, 17335729288925455] "" "Class ", 2953, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 5, 1, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 1, 3, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 5, 3, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 1, 5, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 5, 1, 4], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 1, 3, 4], [1, 0, 0, 1]]} "Class ", 2954, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 5, 1, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 1, 3, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 5, 3, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 1, 5, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 5, 1, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 1, 3, 4], [0, 1, 0, 1]]} "Class ", 2955, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 5, 1, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 1, 3, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 5, 3, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 1, 5, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 5, 1, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 1, 3, 4], [1, 1, 0, 1]]} "Class ", 2956, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 5, 1, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 1, 3, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 5, 3, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 1, 5, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 5, 1, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 1, 3, 4], [0, 0, 1, 1]]} "Class ", 2957, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 5, 1, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 1, 3, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 5, 3, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 1, 5, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 5, 1, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 1, 3, 4], [1, 0, 1, 1]]} "Class ", 2958, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 5, 1, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 1, 3, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 5, 3, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 1, 5, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 5, 1, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 1, 3, 4], [0, 1, 1, 1]]} "Class ", 2959, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 5, 1, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 1, 3, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 5, 3, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 1, 5, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 5, 1, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 1, 3, 4], [1, 1, 1, 1]]} "Class ", 2960, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 5, 4, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 1, 3, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 5, 3, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 1, 2, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 5, 4, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 2, 1, 3, 4], [0, 1, 0, 0]]} "Class ", 2961, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 5, 4, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 1, 3, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 5, 3, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 1, 2, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 5, 4, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 2, 1, 3, 4], [1, 1, 0, 0]]} "Class ", 2962, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 5, 4, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 1, 3, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 5, 3, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 1, 2, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 5, 4, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 2, 1, 3, 4], [0, 0, 1, 0]]} "Class ", 2963, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 5, 4, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 1, 2, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 5, 4, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 1, 0]]} "Class ", 2964, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 5, 4, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 1, 3, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 5, 3, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 1, 2, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 5, 4, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 2, 1, 3, 4], [0, 1, 1, 0]]} "Class ", 2965, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 5, 4, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 1, 3, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 5, 3, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 1, 2, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 5, 4, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 2, 1, 3, 4], [1, 1, 1, 0]]} "Class ", 2966, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 5, 4, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 1, 3, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 5, 3, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 1, 2, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 5, 4, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 2, 1, 3, 4], [0, 1, 0, 1]]} "Class ", 2967, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 5, 4, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 1, 3, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 5, 3, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 1, 2, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 5, 4, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 2, 1, 3, 4], [1, 1, 0, 1]]} "Class ", 2968, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 5, 4, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 1, 3, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 5, 3, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 1, 2, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 5, 4, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 2, 1, 3, 4], [0, 0, 1, 1]]} "Class ", 2969, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 5, 4, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 1, 2, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 5, 4, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 1, 1]]} "Class ", 2970, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 5, 4, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 1, 3, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 5, 3, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 1, 2, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 5, 4, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 2, 1, 3, 4], [0, 1, 1, 1]]} "Class ", 2971, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 5, 4, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 1, 3, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 5, 3, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 3, 1, 2, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 5, 4, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 2, 1, 3, 4], [1, 1, 1, 1]]} "Class ", 2972, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 1, 3, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 2, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 4, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 5, 3, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 1, 3, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 4, 1, 3, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 2, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 4, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 5, 3, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 4, 1, 3, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 286, 1534, 9401, 64822, 496708, 4186954, 38502571, 383567622, 4115069044, 47301470150, 579963450034, 7555366696864, 104215927632308, 1517377966174119, 23255723369554442] "" "Class ", 2973, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 1, 3, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 5, 3, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 1, 3, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 4, 1, 3, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 5, 3, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 4, 1, 3, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1506, 9086, 61461, 460636, 3788565, 33923651, 328504353, 3420711195, 38114650219, 452483293717, 5701713374760, 76005067822065, 1068591450514105, 15803102018183604] "" "Class ", 2974, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 1, 3, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 2, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 4, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 5, 3, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 1, 3, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 5, 2, 4], [0, 1, 0, 0]]} "Class ", 2975, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 1, 3, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 2, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 4, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 5, 3, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 1, 3, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 5, 2, 4], [1, 1, 0, 0]]} "Class ", 2976, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 1, 3, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 2, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 4, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 5, 3, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 1, 3, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 5, 2, 4], [0, 0, 1, 0]]} "Class ", 2977, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 1, 3, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 5, 3, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 1, 3, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 1, 0]]} "Class ", 2978, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 1, 3, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 2, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 4, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 5, 3, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 1, 3, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 5, 2, 4], [0, 1, 1, 0]]} "Class ", 2979, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 1, 3, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 2, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 4, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 5, 3, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 1, 3, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 5, 2, 4], [1, 1, 1, 0]]} "Class ", 2980, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 1, 3, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 2, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 4, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 5, 3, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 1, 3, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 5, 2, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 4, 1, 3, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 2, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 4, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 5, 3, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 3, 5, 2, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 285, 1518, 9204, 62598, 471960, 3906794, 35224338, 343602401, 3605532382, 40497525032, 484789119470, 6161504145790, 82863100203015, 1175612471223550, 17547566383584788] "" "Class ", 2981, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 1, 3, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 5, 3, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 1, 3, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 4, 1, 3, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 5, 3, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 283, 1487, 8829, 58364, 424580, 3367601, 28902781, 266734056, 2632800928, 27667305438, 308315767108, 3630685425127, 45040713990478, 587018676424648, 8017855876809208] "" "Class ", 2982, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 1, 3, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 2, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 4, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 5, 3, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 1, 3, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 5, 2, 4], [0, 1, 0, 1]]} "Class ", 2983, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 1, 3, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 2, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 4, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 5, 3, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 1, 3, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 5, 2, 4], [1, 1, 0, 1]]} "Class ", 2984, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 1, 3, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 2, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 4, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 5, 3, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 1, 3, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 5, 2, 4], [0, 0, 1, 1]]} "Class ", 2985, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 1, 3, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 5, 3, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 1, 3, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 1, 1]]} "Class ", 2986, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 1, 3, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 2, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 4, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 5, 3, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 1, 3, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 5, 2, 4], [0, 1, 1, 1]]} "Class ", 2987, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 1, 3, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 2, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 4, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 5, 3, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 1, 3, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 5, 2, 4], [1, 1, 1, 1]]} "Class ", 2988, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 1, 5, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 5, 2, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 1, 4, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 1, 5, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 4, 1, 5, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 5, 2, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 1, 4, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 4, 1, 5, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 294, 1591, 9799, 67626, 516895, 4334760, 39569513, 390573979, 4145095574, 47067695944, 569386457405, 7310537605958, 99287749637435, 1422155227970191, 21425732316757127] "" "Class ", 2989, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 1, 5, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 5, 2, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 1, 4, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 5, 1, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 1, 5, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 1, 5, 2, 4], [0, 1, 0, 0]]} "Class ", 2990, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 1, 5, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 5, 2, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 1, 4, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 5, 1, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 1, 5, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 1, 5, 2, 4], [1, 1, 0, 0]]} "Class ", 2991, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 1, 5, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 5, 2, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 1, 4, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 5, 1, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 1, 5, 3], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 1, 5, 2, 4], [1, 0, 1, 0]]} "Class ", 2992, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 1, 5, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 5, 2, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 1, 4, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 5, 1, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 1, 5, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 1, 5, 2, 4], [0, 1, 1, 0]]} "Class ", 2993, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 1, 5, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 5, 2, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 1, 4, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 5, 1, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 1, 5, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 1, 5, 2, 4], [1, 1, 1, 0]]} "Class ", 2994, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 1, 5, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 5, 2, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 1, 4, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 5, 1, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 1, 5, 3], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 1, 5, 2, 4], [1, 0, 0, 1]]} "Class ", 2995, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 1, 5, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 5, 2, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 1, 4, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 5, 1, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 1, 5, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 1, 5, 2, 4], [0, 1, 0, 1]]} "Class ", 2996, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 1, 5, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 5, 2, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 1, 4, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 5, 1, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 1, 5, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 1, 5, 2, 4], [1, 1, 0, 1]]} "Class ", 2997, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 1, 5, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 5, 2, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 1, 4, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 5, 1, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 1, 5, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 1, 5, 2, 4], [1, 0, 1, 1]]} "Class ", 2998, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 1, 5, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 5, 2, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 1, 4, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 5, 1, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 1, 5, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 1, 5, 2, 4], [0, 1, 1, 1]]} "Class ", 2999, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 1, 5, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 5, 2, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 1, 4, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 5, 1, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 1, 5, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 1, 5, 2, 4], [1, 1, 1, 1]]} "Class ", 3000, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 3, 1, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 3, 2, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 3, 4, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 3, 5, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 3, 1, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 3, 2, 4], [0, 0, 1, 0]]} "Class ", 3001, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 3, 1, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 3, 5, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 3, 1, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 1, 0]]} "Class ", 3002, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 3, 1, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 3, 2, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 3, 4, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 3, 5, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 3, 1, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 3, 2, 4], [0, 1, 1, 0]]} "Class ", 3003, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 3, 1, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 3, 2, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 3, 4, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 3, 5, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 3, 1, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 3, 2, 4], [1, 1, 1, 0]]} "Class ", 3004, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 3, 1, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 3, 2, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 3, 4, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 3, 5, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 3, 1, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 3, 2, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 4, 3, 1, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 3, 2, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 3, 4, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 3, 5, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 5, 3, 2, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 295, 1609, 10018, 70089, 544299, 4645024, 43205856, 435035048, 4714063339, 54697742738, 676613331189, 8888595247574, 123584020864452, 1813022792495488, 27987656059773377] "" "Class ", 3005, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 3, 1, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 3, 5, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 3, 1, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 4, 3, 1, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 3, 5, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 295, 1604, 9916, 68547, 523304, 4368852, 39572951, 386399425, 4044900095, 45183139949, 536382633600, 6742948014230, 89479991328418, 1249899647730090, 18331330657148828] "" "Class ", 3006, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 3, 1, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 3, 2, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 3, 4, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 3, 5, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 3, 1, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 3, 2, 4], [0, 1, 0, 1]]} "Class ", 3007, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 3, 1, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 3, 2, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 3, 4, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 3, 5, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 3, 1, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 3, 2, 4], [1, 1, 0, 1]]} "Class ", 3008, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 3, 1, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 3, 2, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 3, 4, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 3, 5, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 3, 1, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 3, 2, 4], [0, 0, 1, 1]]} "Class ", 3009, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 3, 1, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 3, 5, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 3, 1, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 1, 1]]} "Class ", 3010, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 3, 1, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 3, 2, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 3, 4, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 3, 5, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 3, 1, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 3, 2, 4], [0, 1, 1, 1]]} "Class ", 3011, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 3, 1, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 3, 2, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 3, 4, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 3, 5, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 3, 1, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 3, 2, 4], [1, 1, 1, 1]]} "Class ", 3012, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 3, 5, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 3, 2, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 3, 4, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 3, 1, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 3, 5, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 3, 2, 4], [0, 0, 1, 0]]} "Class ", 3013, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 3, 5, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 3, 1, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 3, 5, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 1, 0]]} "Class ", 3014, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 3, 5, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 3, 2, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 3, 4, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 3, 1, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 3, 5, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 3, 2, 4], [0, 1, 1, 0]]} "Class ", 3015, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 3, 5, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 3, 2, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 3, 4, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 3, 1, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 3, 5, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 3, 2, 4], [1, 1, 1, 0]]} "Class ", 3016, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 3, 2, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 3, 4, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 3, 1, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 3, 2, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 3, 2, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 3, 4, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 3, 1, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[5, 1, 3, 2, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {}], [[4, 1, 2, 3], {1, 2, 3}, {}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 295, 1604, 9932, 68986, 531163, 4489905, 41334515, 411653367, 4409590818, 50554345673, 617637225127, 8010687937549, 109926220462346, 1591177652239773, 24229570638171517] "" "Class ", 3017, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 3, 1, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 3, 1, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2, 3}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 295, 1602, 9878, 68060, 517723, 4306388, 38862592, 378021097, 3941481630, 43842610670, 518124812615, 6481902594382, 85568121755826, 1188573366307508, 17327479989352203] "" "Class ", 3018, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 3, 2, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 3, 4, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 3, 1, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 3, 2, 4], [0, 1, 0, 1]]} "Class ", 3019, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 3, 2, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 3, 4, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 3, 1, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 3, 2, 4], [1, 1, 0, 1]]} "Class ", 3020, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 3, 5, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 3, 2, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 3, 4, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 3, 1, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 3, 5, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 3, 2, 4], [0, 0, 1, 1]]} "Class ", 3021, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 3, 5, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 3, 1, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 3, 5, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 1, 1]]} "Class ", 3022, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 3, 5, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 3, 2, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 3, 4, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 3, 1, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 3, 5, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 3, 2, 4], [0, 1, 1, 1]]} "Class ", 3023, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 3, 5, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 3, 2, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 3, 4, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 3, 1, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 3, 5, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 3, 2, 4], [1, 1, 1, 1]]} "Class ", 3024, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 1, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 5, 4, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 5, 3], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 5, 1, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 1, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 5, 4, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 5, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 4, 5, 1, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {}, {}], [[2, 3, 4, 1, 5], {1, 2, 3}, {}], [[2, 3, 5, 1, 4], {1, 2, 3}, {}], [[2, 4, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 286, 1539, 9463, 65501, 503826, 4262954, 39349753, 393482832, 4237352767, 48890679177, 601707745019, 7868183963316, 108939870643577, 1592136734744893, 24493468065906059] "" "Class ", 3025, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 1, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 1, 2, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 5, 4, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 5, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 5, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 1, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 1, 2, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 5, 4, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 5, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 4, 5, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 1, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1506, 9060, 60956, 453256, 3690618, 32659736, 312094777, 3202848290, 35130559236, 410127162654, 5077380315708, 66439980004290, 916262342855698, 13282187703082900] "" "Class ", 3026, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 1, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 1, 2, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 5, 4, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 5, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 5, 1, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 5, 1, 2, 4], [0, 1, 0, 0]]} "Class ", 3027, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 1, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 1, 2, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 5, 4, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 5, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 5, 1, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 5, 1, 2, 4], [1, 1, 0, 0]]} "Class ", 3028, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 1, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 1, 2, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 5, 4, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 5, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 5, 1, 3], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[3, 5, 1, 2, 4], [0, 0, 1, 0]]} "Class ", 3029, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 1, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 1, 2, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 5, 4, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 5, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 5, 1, 3], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 5, 1, 2, 4], [1, 0, 1, 0]]} "Class ", 3030, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 1, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 1, 2, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 5, 4, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 5, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 5, 1, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 5, 1, 2, 4], [0, 1, 1, 0]]} "Class ", 3031, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 1, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 1, 2, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 5, 4, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 5, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 5, 1, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 5, 1, 2, 4], [1, 1, 1, 0]]} "Class ", 3032, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 1, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 5, 4, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 5, 3], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 5, 1, 3], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 1, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 5, 4, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 5, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1506, 9064, 61067, 455149, 3717874, 33028289, 317013926, 3269312217, 36051322455, 423292933302, 5272325075253, 69433814820478, 963977067690058, 14071392639755447] "" "Class ", 3033, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 1, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 1, 2, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 5, 4, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 5, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 5, 1, 3], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 5, 1, 2, 4], [1, 0, 0, 1]]} "Class ", 3034, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 1, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 1, 2, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 5, 4, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 5, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 5, 1, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 5, 1, 2, 4], [0, 1, 0, 1]]} "Class ", 3035, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 1, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 1, 2, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 5, 4, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 5, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 5, 1, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 5, 1, 2, 4], [1, 1, 0, 1]]} "Class ", 3036, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 1, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 1, 2, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 5, 4, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 5, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 5, 1, 3], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[3, 5, 1, 2, 4], [0, 0, 1, 1]]} "Class ", 3037, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 1, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 1, 2, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 5, 4, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 5, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 5, 1, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 5, 1, 2, 4], [1, 0, 1, 1]]} "Class ", 3038, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 1, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 1, 2, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 5, 4, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 5, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 5, 1, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 5, 1, 2, 4], [0, 1, 1, 1]]} "Class ", 3039, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 1, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 1, 2, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 5, 4, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 5, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 5, 1, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 5, 1, 2, 4], [1, 1, 1, 1]]} "Class ", 3040, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 3, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 5, 4, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 3, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 5, 3, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 3, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 5, 4, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 3, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 4, 5, 3, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {1, 2, 3}, {}], [[1, 3, 5, 2, 4], {1, 2, 3}, {}], [[1, 4, 5, 2, 3], {1, 2, 3}, {}], [[1, 4, 5, 3, 2], {1, 2, 3, 4}, {}], [[2, 4, 5, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1520, 9312, 64218, 492408, 4153130, 38206944, 380771716, 4086627792, 46992285200, 576396811008, 7511840631612, 103655973202464, 1509814376833260, 23148828107861376] "" "Class ", 3041, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 3, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 3, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 5, 3, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 3, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 3, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 4, 5, 3, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {[1, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 280, 1450, 8486, 55374, 398622, 3137832, 26804894, 246905646, 2439028878, 25717763348, 288273043850, 3422699251030, 42908438019950, 566354174390136, 7850394302843070] "" "Class ", 3042, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 3, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 1, 2, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 5, 4, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 3, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 5, 3, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 3, 1, 2, 4], [0, 1, 0, 0]]} "Class ", 3043, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 3, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 1, 2, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 5, 4, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 3, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 5, 3, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 3, 1, 2, 4], [1, 1, 0, 0]]} "Class ", 3044, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 3, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 1, 2, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 5, 4, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 3, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 5, 3, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 3, 1, 2, 4], [0, 0, 1, 0]]} "Class ", 3045, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 3, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 3, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 5, 3, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 1, 0]]} "Class ", 3046, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 3, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 1, 2, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 5, 4, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 3, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 5, 3, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 3, 1, 2, 4], [0, 1, 1, 0]]} "Class ", 3047, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 3, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 1, 2, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 5, 4, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 3, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 5, 3, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 3, 1, 2, 4], [1, 1, 1, 0]]} "Class ", 3048, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 5, 4, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 3, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 5, 4, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 3, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 282, 1483, 8846, 58982, 434893, 3511886, 30819237, 292040096, 2971488520, 32310342255, 373883672828, 4587314443715, 59482781118852, 812771567869607, 11672145865414898] "" "Class ", 3049, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 3, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 3, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2, 3}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {2}, {}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {1}, {[0, 0, 0, 1, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 278, 1408, 7912, 48639, 323726, 2313771, 17640592, 142681797, 1218678524, 10948964653, 103122539696, 1015206288131, 10419655582692, 111238936481903, 1232757715352112] "" "Class ", 3050, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 1, 2, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 5, 4, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 3, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 3, 1, 2, 4], [0, 1, 0, 1]]} "Class ", 3051, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 1, 2, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 5, 4, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 3, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 3, 1, 2, 4], [1, 1, 0, 1]]} "Class ", 3052, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 3, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 1, 2, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 5, 4, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 3, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 5, 3, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 3, 1, 2, 4], [0, 0, 1, 1]]} "Class ", 3053, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 3, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 3, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 5, 3, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 1, 1]]} "Class ", 3054, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 3, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 1, 2, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 5, 4, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 3, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 5, 3, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 3, 1, 2, 4], [0, 1, 1, 1]]} "Class ", 3055, " is:" {{[[1, 3, 2], [0, 0]], [[2, 4, 5, 3, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 1, 2, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 5, 4, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 2, 1, 3, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 4, 5, 3, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 3, 1, 2, 4], [1, 1, 1, 1]]} "Class ", 3056, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 1, 3, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 1, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 5, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 5, 3, 2], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 1, 3, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 5, 1, 3, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 1, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 5, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 5, 3, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 5, 1, 3, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[2, 4, 1, 3, 5], {1, 2, 3}, {}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 285, 1522, 9275, 63573, 484149, 4055977, 37068904, 367019359, 3913394659, 44707597558, 544800591510, 7053791909079, 96701066669922, 1399332676930049, 21315085669921625] "" "Class ", 3057, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 1, 3, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 1, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 5, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 5, 3, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 1, 3, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 5, 1, 3, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 1, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 5, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 5, 3, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 5, 1, 3, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1504, 9057, 61135, 457239, 3753162, 33543785, 324254003, 3370855502, 37500397376, 444532567927, 5593673737160, 74465603508764, 1045621055636774, 15444721827699049] "" "Class ", 3058, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 1, 3, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 1, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 5, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 5, 3, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 1, 3, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 3, 5, 1, 4], [0, 1, 0, 0]]} "Class ", 3059, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 1, 3, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 1, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 5, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 5, 3, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 1, 3, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 3, 5, 1, 4], [1, 1, 0, 0]]} "Class ", 3060, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 1, 3, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 1, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 5, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 5, 3, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 1, 3, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 3, 5, 1, 4], [0, 0, 1, 0]]} "Class ", 3061, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 1, 3, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 1, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 5, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 5, 3, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 1, 3, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 3, 5, 1, 4], [1, 0, 1, 0]]} "Class ", 3062, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 1, 3, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 1, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 5, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 5, 3, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 1, 3, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 3, 5, 1, 4], [0, 1, 1, 0]]} "Class ", 3063, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 1, 3, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 1, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 5, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 5, 3, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 1, 3, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 3, 5, 1, 4], [1, 1, 1, 0]]} "Class ", 3064, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 1, 3, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 1, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 5, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 5, 3, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 1, 3, 4], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 3, 5, 1, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 5, 1, 3, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 1, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 5, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 5, 3, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[2, 3, 5, 1, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 283, 1491, 8906, 59507, 439844, 3563511, 31404072, 299084358, 3061131294, 33508359143, 390636053765, 4831941123750, 63206735549281, 871789980637995, 12644760168071599] "" "Class ", 3065, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 1, 3, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 1, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 5, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 5, 3, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 1, 3, 4], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 3, 5, 1, 4], [1, 0, 0, 1]]} "Class ", 3066, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 1, 3, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 1, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 5, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 5, 3, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 1, 3, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 3, 5, 1, 4], [0, 1, 0, 1]]} "Class ", 3067, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 1, 3, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 1, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 5, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 5, 3, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 1, 3, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 3, 5, 1, 4], [1, 1, 0, 1]]} "Class ", 3068, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 1, 3, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 1, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 5, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 5, 3, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 1, 3, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 3, 5, 1, 4], [0, 0, 1, 1]]} "Class ", 3069, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 1, 3, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 1, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 5, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 5, 3, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 1, 3, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 3, 5, 1, 4], [1, 0, 1, 1]]} "Class ", 3070, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 1, 3, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 1, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 5, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 5, 3, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 1, 3, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 3, 5, 1, 4], [0, 1, 1, 1]]} "Class ", 3071, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 1, 3, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 1, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 5, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 5, 3, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 1, 3, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 3, 5, 1, 4], [1, 1, 1, 1]]} "Class ", 3072, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 1, 4, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 5, 1, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 1, 5, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 5, 2, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 1, 4, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 5, 1, 4, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 5, 1, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 1, 5, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 5, 2, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 5, 1, 4, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 293, 1574, 9606, 65632, 496229, 4113774, 37104761, 361733726, 3790345852, 42480721771, 507089712938, 6422917444136, 86038307456034, 1215273235194756, 18051735587718251] "" "Class ", 3073, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 1, 4, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 5, 1, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 1, 5, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 5, 2, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 1, 4, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 2, 5, 1, 4], [0, 1, 0, 0]]} "Class ", 3074, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 1, 4, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 5, 1, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 1, 5, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 5, 2, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 1, 4, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 2, 5, 1, 4], [1, 1, 0, 0]]} "Class ", 3075, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 1, 4, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 5, 1, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 1, 5, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 5, 2, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 1, 4, 3], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 2, 5, 1, 4], [1, 0, 1, 0]]} "Class ", 3076, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 1, 4, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 5, 1, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 1, 5, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 5, 2, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 1, 4, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 2, 5, 1, 4], [0, 1, 1, 0]]} "Class ", 3077, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 1, 4, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 5, 1, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 1, 5, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 5, 2, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 1, 4, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 2, 5, 1, 4], [1, 1, 1, 0]]} "Class ", 3078, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 1, 4, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 5, 1, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 1, 5, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 5, 2, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 1, 4, 3], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 2, 5, 1, 4], [1, 0, 0, 1]]} "Class ", 3079, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 1, 4, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 5, 1, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 1, 5, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 5, 2, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 1, 4, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 2, 5, 1, 4], [0, 1, 0, 1]]} "Class ", 3080, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 1, 4, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 5, 1, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 1, 5, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 5, 2, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 1, 4, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 2, 5, 1, 4], [1, 1, 0, 1]]} "Class ", 3081, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 1, 4, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 5, 1, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 1, 5, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 5, 2, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 1, 4, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 2, 5, 1, 4], [1, 0, 1, 1]]} "Class ", 3082, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 1, 4, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 5, 1, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 1, 5, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 5, 2, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 1, 4, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 2, 5, 1, 4], [0, 1, 1, 1]]} "Class ", 3083, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 1, 4, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 5, 1, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 1, 5, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 5, 2, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 1, 4, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 2, 5, 1, 4], [1, 1, 1, 1]]} "Class ", 3084, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 3, 1, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 3, 1, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 3, 5, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 3, 5, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 3, 1, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 3, 1, 4], [0, 0, 1, 0]]} "Class ", 3085, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 3, 1, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 3, 1, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 3, 5, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 3, 5, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 3, 1, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 3, 1, 4], [1, 0, 1, 0]]} "Class ", 3086, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 3, 1, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 3, 1, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 3, 5, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 3, 5, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 3, 1, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 3, 1, 4], [0, 1, 1, 0]]} "Class ", 3087, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 3, 1, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 3, 1, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 3, 5, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 3, 5, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 3, 1, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 3, 1, 4], [1, 1, 1, 0]]} "Class ", 3088, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 3, 1, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 3, 1, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 3, 5, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 3, 5, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 3, 1, 4], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 3, 1, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 5, 3, 1, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 3, 1, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 3, 5, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 3, 5, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[2, 5, 3, 1, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 294, 1596, 9876, 68548, 527525, 4456700, 41002620, 408079325, 4368240029, 50043232720, 610920508928, 7917155227633, 108550854340470, 1569886164694923, 23883496730184205] "" "Class ", 3089, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 3, 1, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 3, 1, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 3, 5, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 3, 5, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 3, 1, 4], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 3, 1, 4], [1, 0, 0, 1]]} "Class ", 3090, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 3, 1, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 3, 1, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 3, 5, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 3, 5, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 3, 1, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 3, 1, 4], [0, 1, 0, 1]]} "Class ", 3091, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 3, 1, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 3, 1, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 3, 5, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 3, 5, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 3, 1, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 3, 1, 4], [1, 1, 0, 1]]} "Class ", 3092, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 3, 1, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 3, 1, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 3, 5, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 3, 5, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 3, 1, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 3, 1, 4], [0, 0, 1, 1]]} "Class ", 3093, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 3, 1, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 3, 1, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 3, 5, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 3, 5, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 3, 1, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 3, 1, 4], [1, 0, 1, 1]]} "Class ", 3094, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 3, 1, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 3, 1, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 3, 5, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 3, 5, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 3, 1, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 3, 1, 4], [0, 1, 1, 1]]} "Class ", 3095, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 3, 1, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 3, 1, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 3, 5, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 3, 5, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 3, 1, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 3, 1, 4], [1, 1, 1, 1]]} "Class ", 3096, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 3, 4, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 3, 1, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 3, 5, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 3, 2, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 3, 4, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 2, 3, 1, 4], [0, 0, 1, 0]]} "Class ", 3097, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 3, 4, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 3, 2, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 3, 4, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 1, 0]]} "Class ", 3098, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 3, 4, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 3, 1, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 3, 5, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 3, 2, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 3, 4, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 2, 3, 1, 4], [0, 1, 1, 0]]} "Class ", 3099, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 3, 4, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 3, 1, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 3, 5, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 3, 2, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 3, 4, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 2, 3, 1, 4], [1, 1, 1, 0]]} "Class ", 3100, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 3, 1, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 3, 5, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 3, 2, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 2, 3, 1, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 3, 1, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 3, 5, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 3, 2, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[5, 2, 3, 1, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {}], [[4, 1, 2, 3], {1, 2, 3}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 294, 1589, 9775, 67431, 515417, 4323853, 39495329, 390178478, 4145147861, 47123113238, 570787303623, 7338616559190, 99814477707507, 1431885422006177, 21606603711870338] "" "Class ", 3101, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 3, 2, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 3, 2, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2, 3}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {2}, {}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 294, 1582, 9613, 64963, 482598, 3904798, 34152671, 320876613, 3221349797, 34399731870, 389210208168, 4649788885217, 58476971211717, 772088743738594, 10676537925275896] "" "Class ", 3102, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 3, 1, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 3, 5, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 3, 2, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 2, 3, 1, 4], [0, 1, 0, 1]]} "Class ", 3103, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 3, 1, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 3, 5, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 3, 2, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 2, 3, 1, 4], [1, 1, 0, 1]]} "Class ", 3104, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 3, 4, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 3, 1, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 3, 5, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 3, 2, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 3, 4, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 2, 3, 1, 4], [0, 0, 1, 1]]} "Class ", 3105, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 3, 4, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 3, 2, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 3, 4, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 1, 1]]} "Class ", 3106, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 3, 4, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 3, 1, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 3, 5, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 3, 2, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 3, 4, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 2, 3, 1, 4], [0, 1, 1, 1]]} "Class ", 3107, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 3, 4, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 3, 1, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 3, 5, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 3, 2, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 3, 4, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 2, 3, 1, 4], [1, 1, 1, 1]]} "Class ", 3108, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 4, 1, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 2, 1, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 4, 5, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 2, 5, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 4, 1, 3], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[3, 5, 2, 1, 4], [0, 0, 1, 0]]} "Class ", 3109, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 4, 1, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 2, 1, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 4, 5, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 2, 5, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 4, 1, 3], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 5, 2, 1, 4], [1, 0, 1, 0]]} "Class ", 3110, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 4, 1, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 2, 1, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 4, 5, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 2, 5, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 4, 1, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 5, 2, 1, 4], [0, 1, 1, 0]]} "Class ", 3111, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 4, 1, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 2, 1, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 4, 5, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 2, 5, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 4, 1, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 5, 2, 1, 4], [1, 1, 1, 0]]} "Class ", 3112, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 4, 1, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 4, 5, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 2, 5, 3], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 4, 1, 3], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 5, 4, 1, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 4, 5, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 2, 5, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 295, 1607, 9986, 69672, 539238, 4584628, 42472103, 425825352, 4593773147, 53056941901, 653211442761, 8539583500996, 118144242629742, 1724495142506369, 26485001360103902] "" "Class ", 3113, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 4, 1, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 2, 1, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 4, 5, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 2, 5, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 4, 1, 3], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 5, 2, 1, 4], [1, 0, 0, 1]]} "Class ", 3114, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 4, 1, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 2, 1, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 4, 5, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 2, 5, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 4, 1, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 5, 2, 1, 4], [0, 1, 0, 1]]} "Class ", 3115, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 4, 1, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 2, 1, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 4, 5, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 2, 5, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 4, 1, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 5, 2, 1, 4], [1, 1, 0, 1]]} "Class ", 3116, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 4, 1, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 2, 1, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 4, 5, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 2, 5, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 4, 1, 3], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[3, 5, 2, 1, 4], [0, 0, 1, 1]]} "Class ", 3117, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 4, 1, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 2, 1, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 4, 5, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 2, 5, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 4, 1, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 5, 2, 1, 4], [1, 0, 1, 1]]} "Class ", 3118, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 4, 1, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 2, 1, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 4, 5, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 2, 5, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 4, 1, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 5, 2, 1, 4], [0, 1, 1, 1]]} "Class ", 3119, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 4, 1, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 2, 1, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 4, 5, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 2, 5, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 4, 1, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 5, 2, 1, 4], [1, 1, 1, 1]]} "Class ", 3120, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 4, 3, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 4, 5, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 2, 3, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 4, 3, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 1, 0]]} "Class ", 3121, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 4, 3, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 2, 3, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 4, 3, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 1, 0]]} "Class ", 3122, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 4, 3, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 2, 1, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 4, 5, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 2, 3, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 4, 3, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 3, 2, 1, 4], [0, 1, 1, 0]]} "Class ", 3123, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 4, 3, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 2, 1, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 4, 5, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 2, 3, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 4, 3, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 3, 2, 1, 4], [1, 1, 1, 0]]} "Class ", 3124, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 295, 1605, 9959, 69424, 537117, 4566691, 42322294, 424616635, 4585117733, 53020495758, 653689063213, 8559660851591, 118635314642512, 1735071627405986, 26703979840934408] "" "Class ", 3125, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2, 3}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {2}, {}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 295, 1601, 9862, 67895, 516232, 4293837, 38766742, 377449511, 3941365017, 43930191943, 520496255019, 6531889417451, 86543767736722, 1207168846437043, 17681613105682349] "" "Class ", 3126, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 2, 1, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 4, 5, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 3, 2, 1, 4], [0, 1, 0, 1]]} "Class ", 3127, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 2, 1, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 4, 5, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 3, 2, 1, 4], [1, 1, 0, 1]]} "Class ", 3128, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 4, 3, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 4, 5, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 2, 3, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 4, 3, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 1, 1]]} "Class ", 3129, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 4, 3, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 2, 3, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 4, 3, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 1, 1]]} "Class ", 3130, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 4, 3, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 2, 1, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 4, 5, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 2, 3, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 4, 3, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 3, 2, 1, 4], [0, 1, 1, 1]]} "Class ", 3131, " is:" {{[[1, 3, 2], [0, 0]], [[2, 5, 4, 3, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 2, 1, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 4, 5, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[4, 1, 2, 3, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 5, 4, 3, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 3, 2, 1, 4], [1, 1, 1, 1]]} "Class ", 3132, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 4, 2, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 4, 2, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {}, {}], [[4, 1, 2, 3], {1, 2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}], [[3, 1, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 3, 5, 2], {1, 2, 3}, {}], [[4, 2, 3, 5, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 286, 1534, 9402, 64845, 497056, 4191611, 38562334, 384336253, 4125181152, 47439128325, 581913475432, 7584183242299, 104660487110810, 1524536370781773, 23375948249875340] "" "Class ", 3133, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 4, 2, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 4, 2, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {1, 2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1508, 9130, 62056, 467907, 3874996, 34961182, 341309265, 3584648126, 40300941788, 482908763660, 6143756532248, 82708143625375, 1174606706775504, 17550327264710565] "" "Class ", 3134, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 4, 2, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 4, 2, 1], [0, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 2, 3, 4, 5], {3}, {}], [[1, 2, 3, 5, 4], {3}, {}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {3}, {}], [[1, 2, 5, 4, 3], {3}, {}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {3}, {}], [[1, 3, 5, 2, 4], {3, 4}, {}], [[1, 3, 5, 4, 2], {3}, {}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {}], [[1, 4, 5, 3, 2], {3}, {}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 5, 1], {3}, {}], [[2, 3, 5, 1, 4], {3, 4}, {}], [[2, 3, 5, 4, 1], {3}, {}], [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[2, 4, 5, 3, 1], {3}, {}], [[2, 5, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1500, 8980, 60050, 443534, 3585086, 31470842, 298093362, 3029974268, 32892762484, 379779893644, 4646702501314, 60052248140066, 817383331414224, 11686984242170144] "" "Class ", 3135, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 2, 1, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 4, 2, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [1, 1, 0, 0]]} "Class ", 3136, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 4, 2, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [0, 0, 1, 0]]} "Class ", 3137, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 4, 2, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 1, 0]]} "Class ", 3138, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 4, 2, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 1, 0]]} "Class ", 3139, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 2, 1, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 4, 2, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [1, 1, 1, 0]]} "Class ", 3140, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {[0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 282, 1474, 8700, 57230, 415344, 3297498, 28436224, 264749068, 2647116054, 28292869356, 321937740072, 3885800108480, 49590067445140, 667191113160566, 9438568805706744] "" "Class ", 3141, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 280, 1438, 8247, 52084, 358492, 2666803, 21295433, 181518218, 1643664403, 15746434714, 159029135193, 1687854259645, 18773787120634, 218299470605303, 2647723649252489] "" "Class ", 3142, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {[0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {1, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 2, 5, 4, 3], {3}, {}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {3, 4}, {}], [[1, 3, 5, 4, 2], {3}, {}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {}], [[1, 4, 5, 3, 2], {3}, {}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3, 4}, {}], [[2, 3, 5, 4, 1], {3}, {}], [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[2, 4, 5, 3, 1], {3}, {}], [[2, 5, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 281, 1451, 8364, 53013, 365379, 2714502, 21586558, 182697496, 1637741278, 15486265957, 153924752099, 1603247199277, 17452387047442, 198078188231694, 2338958674497979] "" "Class ", 3143, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]} "Class ", 3144, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 4, 2, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [0, 0, 1, 1]]} "Class ", 3145, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 4, 2, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 1, 1]]} "Class ", 3146, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 4, 2, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 1, 1]]} "Class ", 3147, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 2, 1, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 4, 2, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 2, 4, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 4, 5, 3], [1, 1, 1, 1]]} "Class ", 3148, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 5, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 4, 5, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 2, 1, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 4, 1, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 2, 5, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 5, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 4, 5, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 2, 1, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 4, 1, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[3, 1, 2, 5, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {1, 2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 293, 1580, 9696, 66685, 508077, 4247629, 38656476, 380417280, 4025231263, 45569936626, 549615559482, 7035454576559, 95262624799311, 1360348514881309, 20431812496231358] "" "Class ", 3149, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 5, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 4, 1, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 2, 5, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 0]]} "Class ", 3150, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 5, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 4, 5, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 2, 1, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 4, 1, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 2, 5, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 4, 5, 3], [1, 1, 0, 0]]} "Class ", 3151, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 5, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 4, 5, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 2, 1, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 4, 1, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 2, 5, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 4, 5, 3], [1, 0, 1, 0]]} "Class ", 3152, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 5, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 4, 1, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 2, 5, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 1, 0]]} "Class ", 3153, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 5, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 4, 5, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 2, 1, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 4, 1, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 2, 5, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 4, 5, 3], [1, 1, 1, 0]]} "Class ", 3154, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 5, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 4, 5, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 2, 1, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 2, 5, 4], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 4, 5, 3], [1, 0, 0, 1]]} "Class ", 3155, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 5, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 2, 5, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]} "Class ", 3156, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 5, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 4, 5, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 2, 1, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 2, 5, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 4, 5, 3], [1, 1, 0, 1]]} "Class ", 3157, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 5, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 4, 5, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 2, 1, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 4, 1, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 2, 5, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 4, 5, 3], [1, 0, 1, 1]]} "Class ", 3158, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 5, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 4, 1, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 2, 5, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 1, 1]]} "Class ", 3159, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 5, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 4, 5, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 2, 1, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 4, 1, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 2, 5, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 4, 5, 3], [1, 1, 1, 1]]} "Class ", 3160, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 4, 2, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 2, 5, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 4, 1, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 4, 2, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 2, 5, 3], [0, 1, 0, 0]]} "Class ", 3161, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 4, 2, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 2, 5, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 4, 1, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 4, 2, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 4, 2, 5, 3], [1, 1, 0, 0]]} "Class ", 3162, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 4, 2, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 2, 5, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 2, 4, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 4, 2, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 2, 5, 3], [0, 0, 1, 0]]} "Class ", 3163, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 4, 2, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 2, 4, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 4, 2, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 1, 0]]} "Class ", 3164, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 4, 2, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 2, 5, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 4, 1, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 2, 4, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 4, 2, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 2, 5, 3], [0, 1, 1, 0]]} "Class ", 3165, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 4, 2, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 2, 5, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 4, 1, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 2, 4, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 4, 2, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 4, 2, 5, 3], [1, 1, 1, 0]]} "Class ", 3166, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 4, 2, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 2, 5, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 4, 1, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 4, 2, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 2, 5, 3], [0, 1, 0, 1]]} "Class ", 3167, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 4, 2, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 2, 5, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 4, 1, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 4, 2, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 4, 2, 5, 3], [1, 1, 0, 1]]} "Class ", 3168, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 4, 2, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 2, 5, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 2, 4, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 4, 2, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 2, 5, 3], [0, 0, 1, 1]]} "Class ", 3169, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 4, 2, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 2, 4, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 4, 2, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 1, 1]]} "Class ", 3170, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 4, 2, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 2, 5, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 4, 1, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 2, 4, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 4, 2, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 2, 5, 3], [0, 1, 1, 1]]} "Class ", 3171, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 4, 2, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 2, 5, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 4, 1, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 2, 4, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 4, 2, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 4, 2, 5, 3], [1, 1, 1, 1]]} "Class ", 3172, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 4, 5, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 5, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 1, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 4, 5, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 1, 4, 5, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 5, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 1, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[3, 1, 4, 5, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}], [[2, 1, 3, 4, 5], {1, 2, 3}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3}, {}], [[3, 1, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 4, 5, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 285, 1530, 9403, 65082, 500793, 4238800, 39134517, 391392607, 4215409630, 48644120989, 598760636650, 7830812507696, 108438715901166, 1585049847685884, 24388083644790752] "" "Class ", 3173, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 4, 5, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 5, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 1, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 4, 5, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 1, 4, 5, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 5, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 1, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[3, 1, 4, 5, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 282, 1483, 8864, 59357, 440333, 3583907, 31747385, 304045075, 3130204917, 34473140553, 404396174984, 5034045700586, 66276705735225, 920116529849069, 13433786730963523] "" "Class ", 3174, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 4, 5, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 5, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 1, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 2, 1, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 4, 5, 2], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 1, 2, 5, 3], [0, 1, 0, 0]]} "Class ", 3175, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 4, 5, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 5, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 1, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 2, 1, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 4, 5, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 2, 5, 3], [1, 1, 0, 0]]} "Class ", 3176, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 4, 5, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 5, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 1, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 2, 1, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 4, 5, 2], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 1, 2, 5, 3], [0, 0, 1, 0]]} "Class ", 3177, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 4, 5, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 5, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 1, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 2, 1, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 4, 5, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 2, 5, 3], [1, 0, 1, 0]]} "Class ", 3178, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 4, 5, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 5, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 1, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 2, 1, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 4, 5, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 1, 2, 5, 3], [0, 1, 1, 0]]} "Class ", 3179, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 4, 5, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 5, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 1, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 2, 1, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 4, 5, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 2, 5, 3], [1, 1, 1, 0]]} "Class ", 3180, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 4, 5, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 5, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 1, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 2, 1, 4], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 4, 5, 2], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 1, 2, 5, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 1, 4, 5, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 5, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 1, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 2, 1, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[4, 1, 2, 5, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 1, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 281, 1463, 8611, 56517, 409136, 3237315, 27786126, 257055989, 2549392532, 26979577095, 303434132326, 3613913062797, 45436182933905, 601324492243455, 8355913898627929] "" "Class ", 3181, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 4, 5, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 5, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 1, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 2, 1, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 4, 5, 2], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 2, 5, 3], [1, 0, 0, 1]]} "Class ", 3182, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 4, 5, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 5, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 1, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 2, 1, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 4, 5, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 1, 2, 5, 3], [0, 1, 0, 1]]} "Class ", 3183, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 4, 5, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 5, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 1, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 2, 1, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 4, 5, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 2, 5, 3], [1, 1, 0, 1]]} "Class ", 3184, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 4, 5, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 5, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 1, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 2, 1, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 4, 5, 2], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 1, 2, 5, 3], [0, 0, 1, 1]]} "Class ", 3185, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 4, 5, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 5, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 1, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 2, 1, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 4, 5, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 2, 5, 3], [1, 0, 1, 1]]} "Class ", 3186, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 4, 5, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 5, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 1, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 2, 1, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 4, 5, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 1, 2, 5, 3], [0, 1, 1, 1]]} "Class ", 3187, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 4, 5, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 2, 5, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 4, 1, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 2, 1, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 4, 5, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 2, 5, 3], [1, 1, 1, 1]]} "Class ", 3188, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 5, 2, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 1, 5, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 5, 1, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 1, 4, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 5, 2, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 4, 1, 5, 3], [0, 1, 0, 0]]} "Class ", 3189, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 5, 2, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 1, 5, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 5, 1, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 1, 4, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 5, 2, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 4, 1, 5, 3], [1, 1, 0, 0]]} "Class ", 3190, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 5, 2, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 1, 5, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 5, 1, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 1, 4, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 5, 2, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 4, 1, 5, 3], [0, 0, 1, 0]]} "Class ", 3191, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 5, 2, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 1, 5, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 5, 1, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 1, 4, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 5, 2, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 4, 1, 5, 3], [1, 0, 1, 0]]} "Class ", 3192, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 5, 2, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 1, 5, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 5, 1, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 1, 4, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 5, 2, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 4, 1, 5, 3], [0, 1, 1, 0]]} "Class ", 3193, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 5, 2, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 1, 5, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 5, 1, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 1, 4, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 5, 2, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 4, 1, 5, 3], [1, 1, 1, 0]]} "Class ", 3194, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 5, 2, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 1, 5, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 5, 1, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 1, 4, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 5, 2, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 4, 1, 5, 3], [0, 1, 0, 1]]} "Class ", 3195, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 5, 2, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 1, 5, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 5, 1, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 1, 4, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 5, 2, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 4, 1, 5, 3], [1, 1, 0, 1]]} "Class ", 3196, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 5, 2, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 1, 5, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 5, 1, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 1, 4, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 5, 2, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 4, 1, 5, 3], [0, 0, 1, 1]]} "Class ", 3197, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 5, 2, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 1, 5, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 5, 1, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 1, 4, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 5, 2, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 4, 1, 5, 3], [1, 0, 1, 1]]} "Class ", 3198, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 5, 2, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 1, 5, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 5, 1, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 1, 4, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 5, 2, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 4, 1, 5, 3], [0, 1, 1, 1]]} "Class ", 3199, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 5, 2, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 1, 5, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 5, 1, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 1, 4, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 5, 2, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 4, 1, 5, 3], [1, 1, 1, 1]]} "Class ", 3200, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 5, 4, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 1, 5, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 5, 1, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 1, 2, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 5, 4, 2], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 2, 1, 5, 3], [0, 1, 0, 0]]} "Class ", 3201, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 5, 4, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 1, 5, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 5, 1, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 1, 2, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 5, 4, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 2, 1, 5, 3], [1, 1, 0, 0]]} "Class ", 3202, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 5, 4, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 1, 5, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 5, 1, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 1, 2, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 5, 4, 2], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 2, 1, 5, 3], [0, 0, 1, 0]]} "Class ", 3203, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 5, 4, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 1, 5, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 5, 1, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 1, 2, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 5, 4, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 2, 1, 5, 3], [1, 0, 1, 0]]} "Class ", 3204, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 5, 4, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 1, 5, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 5, 1, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 1, 2, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 5, 4, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 2, 1, 5, 3], [0, 1, 1, 0]]} "Class ", 3205, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 5, 4, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 1, 5, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 5, 1, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 1, 2, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 5, 4, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 2, 1, 5, 3], [1, 1, 1, 0]]} "Class ", 3206, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 5, 4, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 1, 5, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 5, 1, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 1, 2, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 5, 4, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 2, 1, 5, 3], [0, 1, 0, 1]]} "Class ", 3207, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 5, 4, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 1, 5, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 5, 1, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 1, 2, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 5, 4, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 2, 1, 5, 3], [1, 1, 0, 1]]} "Class ", 3208, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 5, 4, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 1, 5, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 5, 1, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 1, 2, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 5, 4, 2], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 2, 1, 5, 3], [0, 0, 1, 1]]} "Class ", 3209, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 5, 4, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 1, 5, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 5, 1, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 1, 2, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 5, 4, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 2, 1, 5, 3], [1, 0, 1, 1]]} "Class ", 3210, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 5, 4, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 1, 5, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 5, 1, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 1, 2, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 5, 4, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 2, 1, 5, 3], [0, 1, 1, 1]]} "Class ", 3211, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 5, 4, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 1, 5, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 5, 1, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 5, 1, 2, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 5, 4, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 2, 1, 5, 3], [1, 1, 1, 1]]} "Class ", 3212, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 5, 2, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 5, 2, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 287, 1547, 9543, 66290, 511942, 4349791, 40319991, 404880696, 4378339484, 50728250676, 626927210885, 8232143095171, 114454378750676, 1679705680684078, 25948393349062327] "" "Class ", 3213, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 5, 2, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 5, 2, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 286, 1536, 9438, 65258, 501466, 4238588, 39076801, 390215016, 4195703575, 48328976409, 593725027412, 7748972257297, 107073782974103, 1561578829682671, 23970940563665266] "" "Class ", 3214, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 5, 2, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 5, 2, 1], [0, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {3, 4}, {}], [[1, 2, 5, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {3, 4}, {}], [[1, 3, 5, 4, 2], {3}, {}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {}], [[1, 4, 5, 3, 2], {3}, {}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3, 4}, {}], [[2, 3, 5, 4, 1], {3}, {}], [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[2, 4, 5, 3, 1], {3}, {}], [[2, 5, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 285, 1518, 9201, 62555, 471316, 3897361, 35087120, 341587342, 3575466105, 40039073970, 477613161101, 6045851861667, 80940111242112, 1142586221591887, 16961350466186632] "" "Class ", 3215, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 5, 2, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 0]]} "Class ", 3216, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 2, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 5, 2, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [0, 0, 1, 0]]} "Class ", 3217, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 5, 2, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 1, 0]]} "Class ", 3218, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 5, 2, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 1, 0]]} "Class ", 3219, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 5, 2, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 1, 0]]} "Class ", 3220, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {[0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1503, 9029, 60703, 451503, 3680939, 32639854, 312752854, 3220358930, 35462128456, 415865112703, 5174314080184, 68081700671777, 944498880157190, 13778783262676326] "" "Class ", 3221, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {[0, 0, 1, 0, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 283, 1489, 8876, 59065, 433822, 3484776, 30381462, 285669180, 2881284579, 31027096311, 355265623944, 4309794733574, 55215498860368, 744944531959595, 10556690086496290] "" "Class ", 3222, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {}, {[0, 0, 1, 0, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {1, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 2, 5, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {3, 4}, {}], [[1, 3, 5, 4, 2], {1, 3}, {[0, 0, 0, 1, 0, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {}], [[1, 4, 5, 3, 2], {3}, {}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3, 4}, {}], [[2, 3, 5, 4, 1], {1, 3}, {[0, 0, 0, 1, 0, 0]}], [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[2, 4, 5, 3, 1], {3}, {}], [[2, 5, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 282, 1470, 8608, 55800, 395883, 3046411, 25245220, 223957732, 2116382170, 21214414871, 224747136676, 2508427885753, 29412691968151, 361417378077640, 4643569547857672] "" "Class ", 3223, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]} "Class ", 3224, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 2, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 5, 2, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [0, 0, 1, 1]]} "Class ", 3225, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 5, 2, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 1, 1]]} "Class ", 3226, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 5, 2, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 1, 1]]} "Class ", 3227, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 5, 2, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 1, 1]]} "Class ", 3228, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 5, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 5, 4, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 1, 2, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 1, 5, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 5, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 5, 4, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 1, 2, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[3, 2, 1, 5, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 294, 1596, 9890, 68861, 532348, 4524205, 41919783, 420567531, 4541927860, 52532951337, 647881468714, 8486880847396, 117678739403002, 1721927391037734, 26515772934332591] "" "Class ", 3229, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 5, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 5, 1, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 1, 5, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]} "Class ", 3230, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 5, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 5, 4, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 1, 2, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 5, 1, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 1, 5, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 5, 4, 3], [1, 1, 0, 0]]} "Class ", 3231, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 5, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 5, 4, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 1, 2, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 5, 1, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 1, 5, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 5, 4, 3], [1, 0, 1, 0]]} "Class ", 3232, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 5, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 5, 1, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 1, 5, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 1, 0]]} "Class ", 3233, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 5, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 5, 4, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 1, 2, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 5, 1, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 1, 5, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 5, 4, 3], [1, 1, 1, 0]]} "Class ", 3234, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 5, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 5, 4, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 1, 2, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 1, 5, 4], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 5, 4, 3], [1, 0, 0, 1]]} "Class ", 3235, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 5, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 1, 5, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]} "Class ", 3236, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 5, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 5, 4, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 1, 2, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 1, 5, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 5, 4, 3], [1, 1, 0, 1]]} "Class ", 3237, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 5, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 5, 4, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 1, 2, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 5, 1, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 1, 5, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 5, 4, 3], [1, 0, 1, 1]]} "Class ", 3238, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 5, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 5, 1, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 1, 5, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 1, 1]]} "Class ", 3239, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 5, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 1, 5, 4, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 5, 1, 2, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 5, 1, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 1, 5, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 1, 5, 4, 3], [1, 1, 1, 1]]} "Class ", 3240, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 4, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 2, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 4, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 2, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 3}, {}], [[4, 2, 5, 1, 3], {1, 2, 3}, {}], [[4, 3, 5, 1, 2], {1, 2, 3}, {}], [[4, 3, 5, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 290, 1583, 9875, 69318, 540623, 4638043, 43407747, 440111772, 4805560530, 56219641912, 701553329425, 9301698572765, 130583232073795, 1935056550454935, 30183966128655178] "" "Class ", 3241, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 286, 1537, 9419, 64828, 495082, 4154194, 37990595, 376063455, 4005942474, 45690295781, 555540600816, 7173099521279, 98019907356537, 1413236951794800, 21439819699690045] "" "Class ", 3242, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 1, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 4, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 2, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 4, 1, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 2, 4, 3], [0, 1, 0, 0]]} "Class ", 3243, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 1, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 4, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 2, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 4, 1, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 2, 4, 3], [1, 1, 0, 0]]} "Class ", 3244, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 1, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 4, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 2, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 5, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 4, 1, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 2, 4, 3], [0, 0, 1, 0]]} "Class ", 3245, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 1, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 5, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 4, 1, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 1, 0]]} "Class ", 3246, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 1, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 4, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 2, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 5, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 4, 1, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 2, 4, 3], [0, 1, 1, 0]]} "Class ", 3247, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 1, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 4, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 2, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 5, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 4, 1, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 2, 4, 3], [1, 1, 1, 0]]} "Class ", 3248, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 1, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 4, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 2, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 4, 1, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 2, 4, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 1, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 4, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 2, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 5, 2, 4, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 286, 1535, 9395, 64533, 491387, 4107692, 37395426, 368262647, 3900495328, 44212841406, 534027238862, 6847174176764, 92880923217858, 1328924304655596, 20001251853247214] "" "Class ", 3249, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 1, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 4, 1, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 1, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 282, 1473, 8654, 56264, 399950, 3079611, 25494716, 225518995, 2120491416, 21100234542, 221349577730, 2439877207353, 28176473477998, 340024680915781, 4277952067939418] "" "Class ", 3250, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 1, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 4, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 2, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 4, 1, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 2, 4, 3], [0, 1, 0, 1]]} "Class ", 3251, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 1, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 4, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 2, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 4, 1, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 2, 4, 3], [1, 1, 0, 1]]} "Class ", 3252, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 1, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 4, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 2, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 5, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 4, 1, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 2, 4, 3], [0, 0, 1, 1]]} "Class ", 3253, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 1, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 5, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 4, 1, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 1, 1]]} "Class ", 3254, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 1, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 4, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 2, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 4, 1, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 2, 4, 3], [0, 1, 1, 1]]} "Class ", 3255, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 1, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 2, 4, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 4, 2, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 4, 1, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 2, 4, 3], [1, 1, 1, 1]]} "Class ", 3256, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 4, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 2, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 1, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 4, 5, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 4, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 2, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 1, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[3, 2, 4, 5, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}], [[2, 1, 3, 4, 5], {1, 2, 3}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3}, {}], [[3, 1, 4, 5, 2], {1, 2, 3}, {}], [[3, 2, 4, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 286, 1549, 9613, 67128, 520786, 4443114, 41348998, 416889508, 4526596299, 52660894784, 653481240895, 8616002848796, 120282303652150, 1772469724769170, 27493650098386820] "" "Class ", 3257, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 1, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 4, 5, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 1, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[3, 2, 4, 5, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2}, {[1, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 283, 1499, 9043, 61198, 459061, 3778169, 33837736, 327565317, 3407859134, 37915771410, 449218253657, 5646252412185, 75037799922442, 1051293070103651, 15485675437587991] "" "Class ", 3258, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 5, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 4, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 2, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 1, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 4, 5, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 2, 4, 3], [0, 1, 0, 0]]} "Class ", 3259, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 5, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 4, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 2, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 1, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 4, 5, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 2, 4, 3], [1, 1, 0, 0]]} "Class ", 3260, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 5, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 4, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 2, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 1, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 4, 5, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 2, 4, 3], [0, 0, 1, 0]]} "Class ", 3261, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 5, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 1, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 4, 5, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 1, 0]]} "Class ", 3262, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 5, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 4, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 2, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 1, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 4, 5, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 2, 4, 3], [0, 1, 1, 0]]} "Class ", 3263, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 5, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 4, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 2, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 1, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 4, 5, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 2, 4, 3], [1, 1, 1, 0]]} "Class ", 3264, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 5, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 4, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 2, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 1, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 4, 5, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 2, 4, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 5, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 4, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 2, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 1, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[5, 1, 2, 4, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 282, 1483, 8870, 59439, 440708, 3580055, 31616592, 301591668, 3090314074, 33851270035, 394734727760, 4881823944570, 63822855627502, 879451336453937, 12739192446538186] "" "Class ", 3265, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 5, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 1, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 4, 5, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 5, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 1, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2, 3}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {2}, {}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 279, 1422, 8052, 49969, 336473, 2439136, 18915510, 156106297, 1364941043, 12596278898, 122283120092, 1245160569492, 13264896447634, 147505590986815, 1708627117517056] "" "Class ", 3266, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 5, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 4, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 2, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 1, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 4, 5, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 2, 4, 3], [0, 1, 0, 1]]} "Class ", 3267, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 5, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 4, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 2, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 1, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 4, 5, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 2, 4, 3], [1, 1, 0, 1]]} "Class ", 3268, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 5, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 4, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 2, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 1, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 4, 5, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 2, 4, 3], [0, 0, 1, 1]]} "Class ", 3269, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 5, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 1, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 4, 5, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 1, 1]]} "Class ", 3270, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 5, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 4, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 2, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 1, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 4, 5, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 2, 4, 3], [0, 1, 1, 1]]} "Class ", 3271, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 5, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 2, 4, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 4, 2, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 2, 1, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 4, 5, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 2, 4, 3], [1, 1, 1, 1]]} "Class ", 3272, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 1, 4, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 5, 2, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 1, 5, 2], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 1, 4, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 5, 2, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 1, 5, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {}], [[3, 2, 4, 1, 5], {1, 2}, {}], [[3, 2, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {1, 2, 3}, {}], [[4, 3, 5, 1, 2], {1, 2, 3}, {}], [[4, 3, 5, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 289, 1572, 9775, 68411, 532030, 4551493, 42478107, 429473506, 4676184668, 54551887189, 678822667137, 8974945712339, 125640861677209, 1856568933282332, 28878036036271006] "" "Class ", 3273, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 1, 4, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 5, 2, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 1, 5, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 1, 4, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 5, 2, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 1, 5, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 286, 1536, 9407, 64707, 493859, 4141443, 37851711, 374476824, 3986877225, 45449050415, 552328016377, 7128135955028, 97359495318249, 1403074035195090, 21276226164560478] "" "Class ", 3274, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 5, 1, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 1, 4, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 5, 2, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 1, 5, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 5, 1, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 1, 4, 3], [0, 1, 0, 0]]} "Class ", 3275, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 5, 1, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 1, 4, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 5, 2, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 1, 5, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 5, 1, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 1, 4, 3], [1, 1, 0, 0]]} "Class ", 3276, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 5, 1, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 1, 4, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 5, 2, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 1, 5, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 5, 1, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 1, 4, 3], [0, 0, 1, 0]]} "Class ", 3277, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 5, 1, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 1, 4, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 5, 2, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 1, 5, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 5, 1, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 1, 4, 3], [1, 0, 1, 0]]} "Class ", 3278, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 5, 1, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 1, 4, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 5, 2, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 1, 5, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 5, 1, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 1, 4, 3], [0, 1, 1, 0]]} "Class ", 3279, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 5, 1, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 1, 4, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 5, 2, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 1, 5, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 5, 1, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 1, 4, 3], [1, 1, 1, 0]]} "Class ", 3280, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 5, 1, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 1, 4, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 5, 2, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 1, 5, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 5, 1, 4], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 1, 4, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 2, 5, 1, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 1, 4, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 5, 2, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 1, 5, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[2, 5, 1, 4, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 285, 1521, 9240, 62912, 474376, 3923815, 35323661, 343803196, 3597342588, 40267548044, 480145196081, 6075727577313, 81316965707682, 1147690696109014, 17035866772381070] "" "Class ", 3281, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 5, 1, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 1, 4, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 5, 2, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 1, 5, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 5, 1, 4], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 1, 4, 3], [1, 0, 0, 1]]} "Class ", 3282, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 5, 1, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 1, 4, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 5, 2, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 1, 5, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 5, 1, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 1, 4, 3], [0, 1, 0, 1]]} "Class ", 3283, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 5, 1, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 1, 4, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 5, 2, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 1, 5, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 5, 1, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 1, 4, 3], [1, 1, 0, 1]]} "Class ", 3284, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 5, 1, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 1, 4, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 5, 2, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 1, 5, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 5, 1, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 1, 4, 3], [0, 0, 1, 1]]} "Class ", 3285, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 5, 1, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 1, 4, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 5, 2, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 1, 5, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 5, 1, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 1, 4, 3], [1, 0, 1, 1]]} "Class ", 3286, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 5, 1, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 1, 4, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 5, 2, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 1, 5, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 5, 1, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 1, 4, 3], [0, 1, 1, 1]]} "Class ", 3287, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 5, 1, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 1, 4, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 5, 2, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 1, 5, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 5, 1, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 1, 4, 3], [1, 1, 1, 1]]} "Class ", 3288, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 5, 4, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 1, 4, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 5, 2, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 1, 2, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 5, 4, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 2, 1, 4, 3], [0, 1, 0, 0]]} "Class ", 3289, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 5, 4, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 1, 4, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 5, 2, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 1, 2, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 5, 4, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 2, 1, 4, 3], [1, 1, 0, 0]]} "Class ", 3290, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 5, 4, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 1, 4, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 5, 2, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 1, 2, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 5, 4, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 2, 1, 4, 3], [0, 0, 1, 0]]} "Class ", 3291, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 5, 4, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 1, 2, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 5, 4, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 1, 0]]} "Class ", 3292, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 5, 4, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 1, 4, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 5, 2, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 1, 2, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 5, 4, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 2, 1, 4, 3], [0, 1, 1, 0]]} "Class ", 3293, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 5, 4, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 1, 4, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 5, 2, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 1, 2, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 5, 4, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 2, 1, 4, 3], [1, 1, 1, 0]]} "Class ", 3294, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 5, 4, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 1, 4, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 5, 2, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 1, 2, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 5, 4, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 2, 1, 4, 3], [0, 1, 0, 1]]} "Class ", 3295, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 5, 4, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 1, 4, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 5, 2, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 1, 2, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 5, 4, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 2, 1, 4, 3], [1, 1, 0, 1]]} "Class ", 3296, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 5, 4, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 1, 4, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 5, 2, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 1, 2, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 5, 4, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 2, 1, 4, 3], [0, 0, 1, 1]]} "Class ", 3297, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 5, 4, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 1, 2, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 5, 4, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 1, 1]]} "Class ", 3298, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 5, 4, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 1, 4, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 5, 2, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 1, 2, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 5, 4, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 2, 1, 4, 3], [0, 1, 1, 1]]} "Class ", 3299, " is:" {{[[1, 3, 2], [0, 0]], [[3, 2, 5, 4, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 1, 4, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 5, 2, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 4, 1, 2, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 2, 5, 4, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 2, 1, 4, 3], [1, 1, 1, 1]]} "Class ", 3300, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 5, 4, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 5, 4, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3}, {}], [[4, 5, 1, 2, 3], {1, 2, 3}, {}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 287, 1549, 9556, 66344, 511780, 4342665, 40198577, 403108938, 4353304644, 50370803412, 621681058322, 8152398259475, 113194857895202, 1659010403884976, 25594574223471814] "" "Class ", 3301, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 5, 4, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 5, 4, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1506, 9072, 61184, 456546, 3733739, 33208329, 319119746, 3294885114, 36375350149, 427583403061, 5331702573558, 70292418299501, 976938443368733, 14275453603991567] "" "Class ", 3302, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 2, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 2, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 4, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 5, 4, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 1, 2, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 5, 2, 3], [0, 1, 0, 0]]} "Class ", 3303, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 2, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 2, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 4, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 5, 4, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 1, 2, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 4, 5, 2, 3], [1, 1, 0, 0]]} "Class ", 3304, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 2, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 2, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 4, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 5, 4, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 1, 2, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 5, 2, 3], [0, 0, 1, 0]]} "Class ", 3305, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 2, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 5, 4, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 1, 2, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 1, 0]]} "Class ", 3306, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 2, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 2, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 4, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 5, 4, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 1, 2, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 5, 2, 3], [0, 1, 1, 0]]} "Class ", 3307, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 2, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 2, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 4, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 5, 4, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 1, 2, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 4, 5, 2, 3], [1, 1, 1, 0]]} "Class ", 3308, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 2, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 2, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 4, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 5, 4, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 1, 2, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 5, 2, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 2, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 2, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 4, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 5, 4, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 4, 5, 2, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {[0, 0, 1, 0, 0]}], [[2, 3, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 286, 1532, 9350, 64034, 486112, 4050954, 36760709, 360825554, 3808961548, 43028921104, 517943464441, 6617915634494, 89456765088414, 1275414457214556, 19127653985807537] "" "Class ", 3309, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 2, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 5, 4, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 1, 2, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 2, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 5, 4, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2}, {[0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 283, 1486, 8801, 57927, 418801, 3295908, 28028352, 255998393, 2498397842, 25938985243, 285393932109, 3316453153176, 40583083399078, 521557896037540, 7022765613087997] "" "Class ", 3310, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 2, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 2, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 4, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 5, 4, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 1, 2, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 5, 2, 3], [0, 1, 0, 1]]} "Class ", 3311, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 2, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 2, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 4, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 5, 4, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 1, 2, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 4, 5, 2, 3], [1, 1, 0, 1]]} "Class ", 3312, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 2, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 2, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 4, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 5, 4, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 1, 2, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 5, 2, 3], [0, 0, 1, 1]]} "Class ", 3313, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 2, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 5, 4, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 1, 2, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 1, 1]]} "Class ", 3314, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 2, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 2, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 4, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 5, 4, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 1, 2, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 5, 2, 3], [0, 1, 1, 1]]} "Class ", 3315, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 2, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 2, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 4, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 5, 4, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 1, 2, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 4, 5, 2, 3], [1, 1, 1, 1]]} "Class ", 3316, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 5, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 5, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 1, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 1, 5, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 5, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 5, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 1, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[3, 4, 1, 5, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 294, 1591, 9799, 67638, 517092, 4337203, 39599606, 390951647, 4149960294, 47132802148, 570294974990, 7323755960202, 99488296944918, 1425327155027599, 21477989068460292] "" "Class ", 3317, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 5, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 5, 2, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 1, 4, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 5, 1, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 1, 5, 2], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 1, 5, 2, 3], [0, 1, 0, 0]]} "Class ", 3318, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 5, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 5, 2, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 1, 4, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 5, 1, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 1, 5, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 5, 2, 3], [1, 1, 0, 0]]} "Class ", 3319, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 5, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 5, 2, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 1, 4, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 5, 1, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 1, 5, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 5, 2, 3], [1, 0, 1, 0]]} "Class ", 3320, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 5, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 5, 2, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 1, 4, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 5, 1, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 1, 5, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 1, 5, 2, 3], [0, 1, 1, 0]]} "Class ", 3321, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 5, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 5, 2, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 1, 4, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 5, 1, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 1, 5, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 5, 2, 3], [1, 1, 1, 0]]} "Class ", 3322, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 5, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 5, 2, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 1, 4, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 5, 1, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 1, 5, 2], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 5, 2, 3], [1, 0, 0, 1]]} "Class ", 3323, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 5, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 5, 2, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 1, 4, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 5, 1, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 1, 5, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 1, 5, 2, 3], [0, 1, 0, 1]]} "Class ", 3324, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 5, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 5, 2, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 1, 4, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 5, 1, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 1, 5, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 5, 2, 3], [1, 1, 0, 1]]} "Class ", 3325, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 5, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 5, 2, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 1, 4, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 5, 1, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 1, 5, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 5, 2, 3], [1, 0, 1, 1]]} "Class ", 3326, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 5, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 5, 2, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 1, 4, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 5, 1, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 1, 5, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 1, 5, 2, 3], [0, 1, 1, 1]]} "Class ", 3327, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 5, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 5, 2, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 1, 4, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 5, 1, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 1, 5, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 5, 2, 3], [1, 1, 1, 1]]} "Class ", 3328, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 5, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 2, 1, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 5, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[3, 4, 2, 1, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 288, 1563, 9695, 67679, 524936, 4478558, 41682988, 420277084, 4563494745, 53091240881, 658835198328, 8686799350449, 121273618833488, 1787121072632186, 27721582319229407] "" "Class ", 3329, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 5, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 2, 1, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 5, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[3, 4, 2, 1, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1507, 9068, 60989, 453209, 3685888, 32563543, 310510707, 3178269725, 34755288862, 404355731531, 4986922074960, 64986063750051, 892209965685189, 12871852171059069] "" "Class ", 3330, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 1, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 2, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 4, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 5, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 2, 1, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 4, 2, 3], [0, 1, 0, 0]]} "Class ", 3331, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 1, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 2, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 4, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 5, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 2, 1, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 4, 2, 3], [1, 1, 0, 0]]} "Class ", 3332, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 1, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 2, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 4, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 5, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 2, 1, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 4, 2, 3], [0, 0, 1, 0]]} "Class ", 3333, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 1, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 5, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 2, 1, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 1, 0]]} "Class ", 3334, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 1, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 2, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 4, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 5, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 2, 1, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 4, 2, 3], [0, 1, 1, 0]]} "Class ", 3335, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 1, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 2, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 4, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 5, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 2, 1, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 4, 2, 3], [1, 1, 1, 0]]} "Class ", 3336, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 1, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 2, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 4, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 5, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 2, 1, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 4, 2, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 1, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 2, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 4, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 5, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 5, 4, 2, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2}, {[0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 288, 1560, 9648, 67097, 518108, 4398048, 40705733, 407952455, 4401224000, 50856580547, 626633596330, 8201399988611, 113625836615697, 1661303849084041, 25562795268873818] "" "Class ", 3337, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 1, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 5, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 2, 1, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 1, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 5, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {2}, {[0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1505, 9029, 60443, 446371, 3603374, 31567375, 298264230, 3023466606, 32731842018, 376924115205, 4600608054247, 59330997123467, 806158629494427, 11511176410142160] "" "Class ", 3338, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 1, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 2, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 4, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 5, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 2, 1, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 4, 2, 3], [0, 1, 0, 1]]} "Class ", 3339, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 1, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 2, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 4, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 5, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 2, 1, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 4, 2, 3], [1, 1, 0, 1]]} "Class ", 3340, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 1, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 2, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 4, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 5, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 2, 1, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 4, 2, 3], [0, 0, 1, 1]]} "Class ", 3341, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 1, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 5, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 2, 1, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 1, 1]]} "Class ", 3342, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 1, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 2, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 4, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 5, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 2, 1, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 4, 2, 3], [0, 1, 1, 1]]} "Class ", 3343, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 1, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 2, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 4, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 5, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 2, 1, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 4, 2, 3], [1, 1, 1, 1]]} "Class ", 3344, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1522, 9344, 64524, 495168, 4180539, 38498856, 384073125, 4126433364, 47500426361, 583240475968, 7609006612108, 105107048279472, 1532556592708744, 23522185980520672] "" "Class ", 3345, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 283, 1504, 9127, 62147, 469300, 3892958, 35182058, 344060523, 3620207806, 40779634553, 489630325275, 6242323264322, 84217417169326, 1198718633109482, 17951844027175387] "" "Class ", 3346, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 2, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 4, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 1, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 4, 2, 3], [0, 1, 0, 0]]} "Class ", 3347, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 2, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 4, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 1, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 4, 2, 3], [1, 1, 0, 0]]} "Class ", 3348, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 5, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 2, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 4, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 1, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 2, 5, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 4, 2, 3], [0, 0, 1, 0]]} "Class ", 3349, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 5, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 1, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 2, 5, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 1, 0]]} "Class ", 3350, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 5, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 2, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 4, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 1, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 2, 5, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 4, 2, 3], [0, 1, 1, 0]]} "Class ", 3351, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 5, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 2, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 4, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 1, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 2, 5, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 4, 2, 3], [1, 1, 1, 0]]} "Class ", 3352, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 2, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 4, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 1, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 4, 2, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 2, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 4, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 1, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[5, 1, 4, 2, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {}], [[4, 1, 2, 3], {1, 2, 3}, {}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1519, 9282, 63680, 484864, 4057105, 37000424, 365294915, 3881423313, 44162759317, 535717355407, 6901666702752, 94107728597024, 1354018052962627, 20500360473581735] "" "Class ", 3353, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 1, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 1, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2, 3}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {2}, {[0, 0, 1, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 283, 1501, 9059, 61153, 456456, 3731079, 33128725, 317430456, 3263780345, 35834718079, 418375526784, 5174892836528, 67590681843819, 929515458533325, 13423813179818306] "" "Class ", 3354, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 2, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 4, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 1, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 4, 2, 3], [0, 1, 0, 1]]} "Class ", 3355, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 2, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 4, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 1, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 4, 2, 3], [1, 1, 0, 1]]} "Class ", 3356, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 5, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 2, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 4, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 1, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 2, 5, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 4, 2, 3], [0, 0, 1, 1]]} "Class ", 3357, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 5, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 1, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 2, 5, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 1, 1]]} "Class ", 3358, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 2, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 4, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 1, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 4, 2, 3], [0, 1, 1, 1]]} "Class ", 3359, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 2, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 4, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 4, 1, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 4, 2, 3], [1, 1, 1, 1]]} "Class ", 3360, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 5, 4], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 5, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {}, {}], [[2, 3, 4, 1, 5], {1, 2, 3}, {}], [[2, 3, 5, 1, 4], {1, 2, 3}, {}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[3, 4, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 285, 1530, 9393, 64901, 498467, 4210990, 38805945, 387416547, 4165201503, 47979654284, 589534069107, 7696426781911, 106388097187131, 1552309009747716, 23841829868982705] "" "Class ", 3361, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 5, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 5, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 1, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1507, 9068, 60997, 453441, 3690501, 32641785, 311740326, 3197114955, 35043575933, 408819830075, 5057509618747, 66131260796282, 911329705203609, 13200905679512478] "" "Class ", 3362, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 5, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 5, 4], [0, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {}, {}], [[3, 4, 1, 2, 5], {2, 3, 4}, {}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {2, 3, 4}, {}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3}, {}], [[4, 5, 3, 1, 2], {3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 282, 1477, 8750, 57842, 421976, 3365888, 29132668, 271865870, 2720561932, 29057399837, 329890494332, 3966708058696, 50355461759666, 672937948330773, 9442728478186034] "" "Class ", 3363, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 2, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 4, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 5, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 5, 1, 2, 3], [1, 1, 0, 0]]} "Class ", 3364, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 2, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 4, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 5, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 5, 1, 2, 3], [0, 0, 1, 0]]} "Class ", 3365, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 2, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 4, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 5, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 5, 1, 2, 3], [1, 0, 1, 0]]} "Class ", 3366, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 5, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 1, 0]]} "Class ", 3367, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 2, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 4, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 5, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 5, 1, 2, 3], [1, 1, 1, 0]]} "Class ", 3368, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 4, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 5, 4], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 4, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 5, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 283, 1495, 8960, 60102, 446118, 3629301, 32115020, 307079120, 3155187195, 34669073597, 405662001593, 5035905413088, 66106863924267, 914929900719845, 13315193148421613] "" "Class ", 3369, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 2, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 4, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 5, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 5, 1, 2, 3], [1, 0, 0, 1]]} "Class ", 3370, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 5, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 5, 4], [1, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {}, {[0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {}, {}], [[3, 4, 1, 2, 5], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {3}, {[0, 0, 0, 1, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3}, {[0, 0, 0, 1, 0, 0]}], [[4, 5, 3, 1, 2], {3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 280, 1438, 8228, 51720, 353410, 2603104, 20528636, 172357443, 1533307436, 14394266799, 142095767836, 1470515103303, 15910327290814, 179542172694903, 2108622817022452] "" "Class ", 3371, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 2, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 4, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 5, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 5, 1, 2, 3], [1, 1, 0, 1]]} "Class ", 3372, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 2, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 4, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 5, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 5, 1, 2, 3], [0, 0, 1, 1]]} "Class ", 3373, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 2, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 4, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 5, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 5, 1, 2, 3], [1, 0, 1, 1]]} "Class ", 3374, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 5, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]} "Class ", 3375, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 2, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 4, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 5, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 5, 1, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 5, 1, 2, 3], [1, 1, 1, 1]]} "Class ", 3376, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 5, 2, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[3, 4, 5, 2, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {}, {}], [[2, 3, 4, 1, 5], {1, 2, 3}, {}], [[2, 3, 5, 1, 4], {1, 2, 3}, {}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1521, 9328, 64353, 493428, 4162107, 38294880, 381700884, 4097298360, 47123018079, 578092078080, 7535133644385, 103994003442960, 1514978779658625, 23231715753965760] "" "Class ", 3377, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 5, 2, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[3, 4, 5, 2, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 280, 1455, 8598, 56950, 417549, 3355938, 29337902, 277159676, 2813838223, 30551683923, 353262264135, 4333737958128, 56220091497718, 768949034359181, 11059209372469084] "" "Class ", 3378, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 2, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 4, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 5, 2, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 0]]} "Class ", 3379, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 2, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 4, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 5, 2, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 0]]} "Class ", 3380, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 2, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 2, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 4, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 4, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 5, 2, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 4, 1, 2, 3], [0, 0, 1, 0]]} "Class ", 3381, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 2, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 4, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 5, 2, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 1, 0]]} "Class ", 3382, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 2, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 4, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 5, 2, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 0]]} "Class ", 3383, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 2, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 4, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 5, 2, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]} "Class ", 3384, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 4, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 4, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 282, 1483, 8846, 58982, 434893, 3511886, 30819237, 292040096, 2971488520, 32310342255, 373883672828, 4587314443715, 59482781118852, 812771567869607, 11672145865414898] "" "Class ", 3385, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2, 3}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {2}, {}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {[0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 278, 1409, 7936, 48998, 328211, 2365891, 18230842, 149344367, 1294565893, 11827416896, 113500308364, 1140632734055, 11972678179984, 130953382992757, 1489405128787246] "" "Class ", 3386, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]} "Class ", 3387, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]} "Class ", 3388, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 2, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 2, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 4, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 4, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 5, 2, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 4, 1, 2, 3], [0, 0, 1, 1]]} "Class ", 3389, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 2, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 4, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 5, 2, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 1, 1]]} "Class ", 3390, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 2, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 4, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 5, 2, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]} "Class ", 3391, " is:" {{[[1, 3, 2], [0, 0]], [[3, 4, 5, 2, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 4, 5, 2, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]} "Class ", 3392, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 1, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 5, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 5, 4, 2], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 1, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 5, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 5, 4, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[3, 4, 1, 2, 5], {1, 2, 3}, {}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3}, {}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 286, 1537, 9438, 65224, 500882, 4231231, 38993358, 389288370, 4185396840, 48213052737, 592408407574, 7734049009045, 106909469489836, 1559935183134252, 23959255936256050] "" "Class ", 3393, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 1, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 5, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 5, 4, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 1, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 5, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 5, 4, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1505, 9057, 61007, 454576, 3711949, 32962070, 316242218, 3259898830, 35931348752, 421695114348, 5250085002775, 69110571809329, 959075083793516, 13993908920082795] "" "Class ", 3394, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 1, 2, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 1, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 5, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 5, 4, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 1, 2, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 4, 5, 1, 3], [0, 1, 0, 0]]} "Class ", 3395, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 1, 2, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 1, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 5, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 5, 4, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 1, 2, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 4, 5, 1, 3], [1, 1, 0, 0]]} "Class ", 3396, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 1, 2, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 1, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 5, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 5, 4, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 1, 2, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 4, 5, 1, 3], [0, 0, 1, 0]]} "Class ", 3397, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 1, 2, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 1, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 5, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 5, 4, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 1, 2, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 4, 5, 1, 3], [1, 0, 1, 0]]} "Class ", 3398, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 1, 2, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 1, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 5, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 5, 4, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 1, 2, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 4, 5, 1, 3], [0, 1, 1, 0]]} "Class ", 3399, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 1, 2, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 1, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 5, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 5, 4, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 1, 2, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 4, 5, 1, 3], [1, 1, 1, 0]]} "Class ", 3400, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 1, 2, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 1, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 5, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 5, 4, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 1, 2, 4], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 4, 5, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 5, 1, 2, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 1, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 5, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 5, 4, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[2, 4, 5, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1506, 9069, 61148, 456220, 3730939, 33184463, 318903694, 3292760996, 36352247123, 427302652580, 5327905147841, 70235834740773, 976024141282794, 14259674211631782] "" "Class ", 3401, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 1, 2, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 1, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 5, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 5, 4, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 1, 2, 4], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 4, 5, 1, 3], [1, 0, 0, 1]]} "Class ", 3402, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 1, 2, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 1, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 5, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 5, 4, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 1, 2, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 4, 5, 1, 3], [0, 1, 0, 1]]} "Class ", 3403, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 1, 2, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 1, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 5, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 5, 4, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 1, 2, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 4, 5, 1, 3], [1, 1, 0, 1]]} "Class ", 3404, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 1, 2, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 1, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 5, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 5, 4, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 1, 2, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 4, 5, 1, 3], [0, 0, 1, 1]]} "Class ", 3405, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 1, 2, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 1, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 5, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 5, 4, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 1, 2, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 4, 5, 1, 3], [1, 0, 1, 1]]} "Class ", 3406, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 1, 2, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 1, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 5, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 5, 4, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 1, 2, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 4, 5, 1, 3], [0, 1, 1, 1]]} "Class ", 3407, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 1, 2, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 1, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 5, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 5, 4, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 1, 2, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 4, 5, 1, 3], [1, 1, 1, 1]]} "Class ", 3408, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 1, 4, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 5, 1, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 1, 5, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 5, 2, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 1, 4, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 5, 1, 4, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 5, 1, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 1, 5, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 5, 2, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[3, 5, 1, 4, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 293, 1574, 9606, 65654, 496675, 4119916, 37182085, 362704308, 3802778920, 42644899336, 509339063845, 6454992461518, 86514788931192, 1222647123835253, 18170568024182255] "" "Class ", 3409, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 1, 4, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 5, 1, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 1, 5, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 5, 2, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 1, 4, 2], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 2, 5, 1, 3], [0, 1, 0, 0]]} "Class ", 3410, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 1, 4, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 5, 1, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 1, 5, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 5, 2, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 1, 4, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 2, 5, 1, 3], [1, 1, 0, 0]]} "Class ", 3411, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 1, 4, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 5, 1, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 1, 5, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 5, 2, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 1, 4, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 2, 5, 1, 3], [1, 0, 1, 0]]} "Class ", 3412, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 1, 4, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 5, 1, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 1, 5, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 5, 2, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 1, 4, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 2, 5, 1, 3], [0, 1, 1, 0]]} "Class ", 3413, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 1, 4, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 5, 1, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 1, 5, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 5, 2, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 1, 4, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 2, 5, 1, 3], [1, 1, 1, 0]]} "Class ", 3414, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 1, 4, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 5, 1, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 1, 5, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 5, 2, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 1, 4, 2], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 2, 5, 1, 3], [1, 0, 0, 1]]} "Class ", 3415, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 1, 4, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 5, 1, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 1, 5, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 5, 2, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 1, 4, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 2, 5, 1, 3], [0, 1, 0, 1]]} "Class ", 3416, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 1, 4, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 5, 1, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 1, 5, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 5, 2, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 1, 4, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 2, 5, 1, 3], [1, 1, 0, 1]]} "Class ", 3417, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 1, 4, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 5, 1, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 1, 5, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 5, 2, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 1, 4, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 2, 5, 1, 3], [1, 0, 1, 1]]} "Class ", 3418, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 1, 4, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 5, 1, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 1, 5, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 5, 2, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 1, 4, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 2, 5, 1, 3], [0, 1, 1, 1]]} "Class ", 3419, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 1, 4, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 5, 1, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 1, 5, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 5, 2, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 1, 4, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 2, 5, 1, 3], [1, 1, 1, 1]]} "Class ", 3420, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 1, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 5, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 5, 2], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 1, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 5, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 5, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 287, 1551, 9576, 66537, 513696, 4362362, 40414585, 405612115, 4383980410, 50768039499, 627104822108, 8230365796562, 114372518942335, 1677665171521125, 25903910299433676] "" "Class ", 3421, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 1, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 5, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 5, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 1, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 5, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 5, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1507, 9068, 60989, 453209, 3685888, 32563543, 310510707, 3178269725, 34755288862, 404355731531, 4986922074960, 64986063750051, 892209965685189, 12871852171059069] "" "Class ", 3422, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 1, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 1, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 5, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 5, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 2, 1, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 4, 1, 3], [0, 1, 0, 0]]} "Class ", 3423, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 1, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 1, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 5, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 5, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 2, 1, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 4, 1, 3], [1, 1, 0, 0]]} "Class ", 3424, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 1, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 1, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 5, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 5, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 2, 1, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 4, 1, 3], [0, 0, 1, 0]]} "Class ", 3425, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 1, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 1, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 5, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 5, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 2, 1, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 4, 1, 3], [1, 0, 1, 0]]} "Class ", 3426, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 1, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 1, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 5, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 5, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 2, 1, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 4, 1, 3], [0, 1, 1, 0]]} "Class ", 3427, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 1, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 1, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 5, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 5, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 2, 1, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 4, 1, 3], [1, 1, 1, 0]]} "Class ", 3428, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 1, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 1, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 5, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 5, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 2, 1, 4], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 4, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 1, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 1, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 5, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 5, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[2, 5, 4, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 286, 1536, 9403, 64653, 493187, 4132578, 37734932, 372913970, 3965476737, 45147254468, 547918389568, 7061236158551, 96304506956503, 1385775157823716, 20981362228910476] "" "Class ", 3429, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 1, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 1, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 5, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 5, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 2, 1, 4], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 4, 1, 3], [1, 0, 0, 1]]} "Class ", 3430, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 1, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 1, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 5, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 5, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 2, 1, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 4, 1, 3], [0, 1, 0, 1]]} "Class ", 3431, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 1, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 1, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 5, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 5, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 2, 1, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 4, 1, 3], [1, 1, 0, 1]]} "Class ", 3432, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 1, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 1, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 5, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 5, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 2, 1, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 4, 1, 3], [0, 0, 1, 1]]} "Class ", 3433, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 1, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 1, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 5, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 5, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 2, 1, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 4, 1, 3], [1, 0, 1, 1]]} "Class ", 3434, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 1, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 1, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 5, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 5, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 2, 1, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 4, 1, 3], [0, 1, 1, 1]]} "Class ", 3435, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 1, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 1, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 5, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 5, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 2, 1, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 4, 1, 3], [1, 1, 1, 1]]} "Class ", 3436, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 5, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 2, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 5, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 2, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[2, 4, 1, 3, 5], {1, 2, 3}, {}], [[2, 5, 1, 3, 4], {1, 2, 3}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1523, 9360, 64693, 496868, 4198512, 38697976, 386387436, 4154834800, 47868332828, 588260209568, 7681050110843, 106192935177560, 1549713458906552, 23805844072171544] "" "Class ", 3437, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 2, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 2, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {[1, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 282, 1488, 8956, 60452, 452104, 3711537, 33180840, 320847281, 3336607866, 37133636236, 440363716321, 5543533650884, 73829473279293, 1037132622021693, 15325907281234770] "" "Class ", 3438, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 1, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 5, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 2, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 2, 4, 1, 3], [0, 1, 0, 0]]} "Class ", 3439, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 1, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 5, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 2, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 2, 4, 1, 3], [1, 1, 0, 0]]} "Class ", 3440, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 4, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 5, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 2, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 2, 4, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 1, 0]]} "Class ", 3441, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 4, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 2, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 2, 4, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 1, 0]]} "Class ", 3442, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 4, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 1, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 5, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 2, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 2, 4, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 2, 4, 1, 3], [0, 1, 1, 0]]} "Class ", 3443, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 4, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 1, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 5, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 2, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 2, 4, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 2, 4, 1, 3], [1, 1, 1, 0]]} "Class ", 3444, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 5, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 2, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 5, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 2, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {}], [[4, 1, 2, 3], {1, 2, 3}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 283, 1505, 9144, 62342, 471461, 3917723, 35472118, 347559396, 3664207375, 41358302952, 497590291216, 6356875609790, 85941383171292, 1225822366529861, 18396476665551878] "" "Class ", 3445, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 2, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 2, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2, 3}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {2}, {}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2}, {[0, 0, 1, 0, 0]}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 281, 1467, 8672, 57109, 414004, 3273884, 28027474, 258100172, 2542899429, 26680569646, 296919743081, 3492446321492, 43282667506856, 563621488035116, 7692563986587578] "" "Class ", 3446, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 1, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 5, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 2, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 2, 4, 1, 3], [0, 1, 0, 1]]} "Class ", 3447, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 1, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 5, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 2, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 2, 4, 1, 3], [1, 1, 0, 1]]} "Class ", 3448, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 4, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 5, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 2, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 2, 4, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 1, 1]]} "Class ", 3449, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 4, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 2, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 2, 4, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 1, 1]]} "Class ", 3450, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 4, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 1, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 5, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 2, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 2, 4, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 2, 4, 1, 3], [0, 1, 1, 1]]} "Class ", 3451, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 2, 4, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 1, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 5, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 4, 2, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 2, 4, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 2, 4, 1, 3], [1, 1, 1, 1]]} "Class ", 3452, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 4, 1, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 2, 1, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 4, 5, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 2, 5, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 4, 1, 2], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 5, 2, 1, 3], [0, 0, 1, 0]]} "Class ", 3453, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 4, 1, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 2, 1, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 4, 5, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 2, 5, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 4, 1, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 5, 2, 1, 3], [1, 0, 1, 0]]} "Class ", 3454, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 4, 1, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 2, 5, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 4, 1, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 1, 0]]} "Class ", 3455, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 4, 1, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 2, 1, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 4, 5, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 2, 5, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 4, 1, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 5, 2, 1, 3], [1, 1, 1, 0]]} "Class ", 3456, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 4, 5, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 2, 5, 4], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 4, 5, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 2, 5, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 295, 1606, 9972, 69527, 537776, 4569546, 42309793, 423982739, 4571668910, 52776968734, 649471911410, 8487003768193, 117367459634142, 1712459931688181, 26289797062653995] "" "Class ", 3457, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 2, 1, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 4, 5, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 2, 5, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 5, 2, 1, 3], [1, 0, 0, 1]]} "Class ", 3458, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 2, 5, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 2, 5, 4], [1, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {}, {[0, 0, 1, 0, 0]}], [[3, 4, 1, 2, 5], {2, 3, 4}, {}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {2, 3, 4}, {}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {}], [[4, 5, 1, 3, 2], {3}, {[0, 0, 0, 1, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3}, {[0, 0, 0, 1, 0, 0]}], [[4, 5, 3, 1, 2], {3}, {[0, 0, 0, 1, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 295, 1601, 9853, 67639, 511573, 4221613, 37713621, 362360004, 3724075184, 40746758291, 472716341298, 5794297881990, 74805962664827, 1014380547654186, 14411729716055131] "" "Class ", 3459, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 2, 1, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 4, 5, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 2, 5, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 5, 2, 1, 3], [1, 1, 0, 1]]} "Class ", 3460, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 4, 1, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 2, 1, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 4, 5, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 2, 5, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 4, 1, 2], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 5, 2, 1, 3], [0, 0, 1, 1]]} "Class ", 3461, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 4, 1, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 2, 1, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 4, 5, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 2, 5, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 4, 1, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 5, 2, 1, 3], [1, 0, 1, 1]]} "Class ", 3462, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 4, 1, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 2, 5, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 4, 1, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]} "Class ", 3463, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 4, 1, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 2, 1, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 4, 5, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 2, 5, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 4, 1, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 5, 2, 1, 3], [1, 1, 1, 1]]} "Class ", 3464, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 4, 2, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 4, 5, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 2, 4, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 4, 2, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 1, 0]]} "Class ", 3465, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 4, 2, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 2, 4, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 4, 2, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 1, 0]]} "Class ", 3466, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 4, 2, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 2, 4, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 4, 2, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 1, 0]]} "Class ", 3467, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 4, 2, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 2, 1, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 4, 5, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 2, 4, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 4, 2, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 4, 2, 1, 3], [1, 1, 1, 0]]} "Class ", 3468, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {}], [[4, 3, 2, 1], {1}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 295, 1605, 9959, 69424, 537117, 4566691, 42322294, 424616635, 4585117733, 53020495758, 653689063213, 8559660851591, 118635314642512, 1735071627405986, 26703979840934408] "" "Class ", 3469, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2, 3}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {2}, {}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 295, 1600, 9842, 67642, 513404, 4262617, 38415142, 373355906, 3891760539, 43302947904, 512211628965, 6417590407710, 84897511034114, 1182436526467770, 17294445149063652] "" "Class ", 3470, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]} "Class ", 3471, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]} "Class ", 3472, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 4, 2, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 4, 5, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 2, 4, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 4, 2, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 1, 1]]} "Class ", 3473, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 4, 2, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 2, 4, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 4, 2, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 1, 1]]} "Class ", 3474, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 4, 2, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 2, 4, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 4, 2, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 1, 1]]} "Class ", 3475, " is:" {{[[1, 3, 2], [0, 0]], [[3, 5, 4, 2, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 2, 1, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 4, 5, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 1, 2, 4, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[3, 5, 4, 2, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 4, 2, 1, 3], [1, 1, 1, 1]]} "Class ", 3476, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 2, 3, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 4, 3, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 2, 3, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 1, 2, 3, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 4, 3, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 1, 2, 3, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3}, {}], [[5, 2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 287, 1546, 9522, 66004, 508378, 4307466, 39814017, 398663723, 4298943521, 49668272004, 612104247596, 8014950563196, 111121958384924, 1626222838108737, 25051665858422189] "" "Class ", 3477, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 2, 3, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 4, 3, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 2, 3, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 1, 2, 3, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 4, 3, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 1, 2, 3, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1505, 9072, 61244, 457639, 3748688, 33396566, 321471868, 3324735840, 36765418596, 432862449991, 5405903715813, 71377019684093, 993429289042396, 14536205422741255] "" "Class ", 3478, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 2, 3, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 4, 5, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 2, 1, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 4, 3, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 2, 3, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 4, 5, 2], [0, 1, 0, 0]]} "Class ", 3479, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 2, 3, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 4, 5, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 2, 1, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 4, 3, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 2, 3, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 4, 5, 2], [1, 1, 0, 0]]} "Class ", 3480, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 2, 3, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 4, 5, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 4, 3, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 2, 3, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 4, 5, 2], [0, 0, 1, 0]]} "Class ", 3481, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 2, 3, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 4, 3, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 2, 3, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 1, 0]]} "Class ", 3482, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 2, 3, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 4, 5, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 2, 1, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 4, 3, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 2, 3, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 4, 5, 2], [0, 1, 1, 0]]} "Class ", 3483, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 2, 3, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 4, 5, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 2, 1, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 4, 3, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 2, 3, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 4, 5, 2], [1, 1, 1, 0]]} "Class ", 3484, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {[0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 283, 1490, 8885, 59178, 435423, 3507058, 30689530, 289930214, 2940889023, 31878065068, 367734681262, 4497986982328, 58147553571975, 792157054314956, 11342818024511068] "" "Class ", 3485, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {[0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 281, 1454, 8430, 53964, 377186, 2852895, 23181710, 201162476, 1854862462, 18096147848, 186109871200, 2011240744847, 22773998356904, 269526819758609, 3326402252712412] "" "Class ", 3486, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 4, 5, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 2, 1, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 4, 5, 2], [0, 1, 0, 1]]} "Class ", 3487, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 4, 5, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 2, 1, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 4, 5, 2], [1, 1, 0, 1]]} "Class ", 3488, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 2, 3, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 4, 5, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 4, 3, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 2, 3, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 4, 5, 2], [0, 0, 1, 1]]} "Class ", 3489, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 2, 3, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 4, 3, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 2, 3, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 1, 1]]} "Class ", 3490, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 2, 3, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 4, 5, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 2, 1, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 4, 3, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 2, 3, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 4, 5, 2], [0, 1, 1, 1]]} "Class ", 3491, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 2, 3, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 4, 5, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 2, 1, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 4, 3, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 2, 3, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 4, 5, 2], [1, 1, 1, 1]]} "Class ", 3492, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 2, 5, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 4, 5, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 2, 1, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 4, 1, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 2, 5, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 1, 2, 5, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 4, 5, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 2, 1, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 4, 1, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 1, 2, 5, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2}, {[0, 0, 1, 0, 0]}], [[4, 1, 2, 3], {1, 2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 293, 1580, 9692, 66632, 507387, 4238756, 38544834, 379001379, 4006821885, 45322629805, 546168324275, 6985477932221, 94508317558911, 1348494491771973, 20237918943943173] "" "Class ", 3493, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 2, 5, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 4, 5, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 2, 1, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 4, 1, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 2, 5, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 1, 4, 5, 2], [0, 1, 0, 0]]} "Class ", 3494, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 2, 5, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 4, 5, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 2, 1, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 4, 1, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 2, 5, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 1, 4, 5, 2], [1, 1, 0, 0]]} "Class ", 3495, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 2, 5, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 4, 5, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 2, 1, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 4, 1, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 2, 5, 3], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 1, 4, 5, 2], [1, 0, 1, 0]]} "Class ", 3496, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 2, 5, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 4, 5, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 2, 1, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 4, 1, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 2, 5, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 1, 4, 5, 2], [0, 1, 1, 0]]} "Class ", 3497, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 2, 5, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 4, 5, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 2, 1, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 4, 1, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 2, 5, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 1, 4, 5, 2], [1, 1, 1, 0]]} "Class ", 3498, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 2, 5, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 4, 5, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 2, 1, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 4, 1, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 2, 5, 3], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 1, 4, 5, 2], [1, 0, 0, 1]]} "Class ", 3499, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 2, 5, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 4, 5, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 2, 1, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 4, 1, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 2, 5, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 1, 4, 5, 2], [0, 1, 0, 1]]} "Class ", 3500, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 2, 5, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 4, 5, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 2, 1, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 4, 1, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 2, 5, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 1, 4, 5, 2], [1, 1, 0, 1]]} "Class ", 3501, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 2, 5, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 4, 5, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 2, 1, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 4, 1, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 2, 5, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 1, 4, 5, 2], [1, 0, 1, 1]]} "Class ", 3502, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 2, 5, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 4, 5, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 2, 1, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 4, 1, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 2, 5, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 1, 4, 5, 2], [0, 1, 1, 1]]} "Class ", 3503, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 2, 5, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 4, 5, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 2, 1, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 4, 1, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 2, 5, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 1, 4, 5, 2], [1, 1, 1, 1]]} "Class ", 3504, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 3, 2, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 3, 5, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 3, 1, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 3, 4, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 3, 2, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 3, 5, 2], [0, 1, 0, 0]]} "Class ", 3505, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 3, 2, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 3, 5, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 3, 1, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 3, 4, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 3, 2, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 4, 3, 5, 2], [1, 1, 0, 0]]} "Class ", 3506, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 3, 2, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 3, 5, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 3, 1, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 3, 4, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 3, 2, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 3, 5, 2], [0, 0, 1, 0]]} "Class ", 3507, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 3, 2, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 3, 4, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 3, 2, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 1, 0]]} "Class ", 3508, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 3, 2, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 3, 5, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 3, 1, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 3, 4, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 3, 2, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 3, 5, 2], [0, 1, 1, 0]]} "Class ", 3509, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 3, 2, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 3, 5, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 3, 1, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 3, 4, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 3, 2, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 4, 3, 5, 2], [1, 1, 1, 0]]} "Class ", 3510, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 3, 2, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 3, 5, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 3, 1, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 3, 2, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 3, 5, 2], [0, 1, 0, 1]]} "Class ", 3511, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 3, 2, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 3, 5, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 3, 1, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 3, 2, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 4, 3, 5, 2], [1, 1, 0, 1]]} "Class ", 3512, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 3, 2, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 3, 5, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 3, 1, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 3, 4, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 3, 2, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 3, 5, 2], [0, 0, 1, 1]]} "Class ", 3513, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 3, 2, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 3, 4, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 3, 2, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 1, 1]]} "Class ", 3514, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 3, 2, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 3, 5, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 3, 1, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 3, 4, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 3, 2, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 3, 5, 2], [0, 1, 1, 1]]} "Class ", 3515, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 3, 2, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 3, 5, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 3, 1, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 3, 4, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 3, 2, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 4, 3, 5, 2], [1, 1, 1, 1]]} "Class ", 3516, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 3, 5, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 3, 5, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 3, 1, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 3, 1, 4], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 3, 5, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 1, 3, 5, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 3, 5, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 3, 1, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 3, 1, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 1, 3, 5, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {1, 2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 285, 1529, 9390, 64914, 498748, 4215211, 38860880, 388108654, 4174240425, 48102292820, 591267282032, 7722029171324, 106783133889749, 1558672564773266, 23948784035364229] "" "Class ", 3517, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 3, 5, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 3, 5, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 3, 1, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 3, 1, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 3, 5, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 1, 3, 5, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 3, 5, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 3, 1, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 3, 1, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 1, 3, 5, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 283, 1500, 9069, 61557, 463400, 3831215, 34506624, 336293293, 3526024184, 39576965871, 473479855768, 6014507273109, 80847069647598, 1146511409456430, 17106469679376414] "" "Class ", 3518, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 3, 5, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 3, 5, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 3, 1, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 3, 1, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 3, 5, 2], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 1, 3, 5, 2], [0, 1, 0, 0]]} "Class ", 3519, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 3, 5, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 3, 5, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 3, 1, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 3, 1, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 3, 5, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 3, 5, 2], [1, 1, 0, 0]]} "Class ", 3520, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 3, 5, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 3, 5, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 3, 1, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 3, 1, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 3, 5, 2], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 1, 3, 5, 2], [0, 0, 1, 0]]} "Class ", 3521, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 3, 5, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 3, 5, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 3, 1, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 3, 1, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 3, 5, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 3, 5, 2], [1, 0, 1, 0]]} "Class ", 3522, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 3, 5, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 3, 5, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 3, 1, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 3, 1, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 3, 5, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 1, 3, 5, 2], [0, 1, 1, 0]]} "Class ", 3523, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 3, 5, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 3, 5, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 3, 1, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 3, 1, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 3, 5, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 3, 5, 2], [1, 1, 1, 0]]} "Class ", 3524, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 3, 5, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 3, 5, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 3, 1, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 3, 1, 4], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 3, 5, 2], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 1, 3, 5, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 1, 3, 5, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 3, 5, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 3, 1, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 3, 1, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[4, 1, 3, 5, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 281, 1463, 8611, 56517, 409136, 3237315, 27786126, 257055989, 2549392532, 26979577095, 303434132326, 3613913062797, 45436182933905, 601324492243455, 8355913898627929] "" "Class ", 3525, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 3, 5, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 3, 5, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 3, 1, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 3, 1, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 3, 5, 2], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 3, 5, 2], [1, 0, 0, 1]]} "Class ", 3526, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 3, 5, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 3, 5, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 3, 1, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 3, 1, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 3, 5, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 1, 3, 5, 2], [0, 1, 0, 1]]} "Class ", 3527, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 3, 5, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 3, 5, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 3, 1, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 3, 1, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 3, 5, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 3, 5, 2], [1, 1, 0, 1]]} "Class ", 3528, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 3, 5, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 3, 5, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 3, 1, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 3, 1, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 3, 5, 2], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 1, 3, 5, 2], [0, 0, 1, 1]]} "Class ", 3529, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 3, 5, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 3, 5, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 3, 1, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 3, 1, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 3, 5, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 3, 5, 2], [1, 0, 1, 1]]} "Class ", 3530, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 3, 5, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 3, 5, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 3, 1, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 3, 1, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 3, 5, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 1, 3, 5, 2], [0, 1, 1, 1]]} "Class ", 3531, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 3, 5, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 3, 5, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 3, 1, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 3, 1, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 3, 5, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 3, 5, 2], [1, 1, 1, 1]]} "Class ", 3532, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 5, 2, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 1, 5, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 5, 1, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 1, 4, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 5, 2, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 4, 1, 5, 2], [0, 1, 0, 0]]} "Class ", 3533, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 5, 2, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 1, 5, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 5, 1, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 1, 4, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 5, 2, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 4, 1, 5, 2], [1, 1, 0, 0]]} "Class ", 3534, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 5, 2, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 1, 5, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 5, 1, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 1, 4, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 5, 2, 3], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[3, 4, 1, 5, 2], [0, 0, 1, 0]]} "Class ", 3535, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 5, 2, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 1, 5, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 5, 1, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 1, 4, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 5, 2, 3], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 4, 1, 5, 2], [1, 0, 1, 0]]} "Class ", 3536, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 5, 2, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 1, 5, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 5, 1, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 1, 4, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 5, 2, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 4, 1, 5, 2], [0, 1, 1, 0]]} "Class ", 3537, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 5, 2, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 1, 5, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 5, 1, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 1, 4, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 5, 2, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 4, 1, 5, 2], [1, 1, 1, 0]]} "Class ", 3538, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 5, 2, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 1, 5, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 5, 1, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 1, 4, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 5, 2, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 4, 1, 5, 2], [0, 1, 0, 1]]} "Class ", 3539, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 5, 2, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 1, 5, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 5, 1, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 1, 4, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 5, 2, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 4, 1, 5, 2], [1, 1, 0, 1]]} "Class ", 3540, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 5, 2, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 1, 5, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 5, 1, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 1, 4, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 5, 2, 3], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[3, 4, 1, 5, 2], [0, 0, 1, 1]]} "Class ", 3541, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 5, 2, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 1, 5, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 5, 1, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 1, 4, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 5, 2, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 4, 1, 5, 2], [1, 0, 1, 1]]} "Class ", 3542, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 5, 2, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 1, 5, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 5, 1, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 1, 4, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 5, 2, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 4, 1, 5, 2], [0, 1, 1, 1]]} "Class ", 3543, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 5, 2, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 1, 5, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 5, 1, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 1, 4, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 5, 2, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 4, 1, 5, 2], [1, 1, 1, 1]]} "Class ", 3544, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 5, 3, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 1, 5, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 5, 1, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 1, 3, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 5, 3, 2], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 3, 1, 5, 2], [0, 1, 0, 0]]} "Class ", 3545, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 5, 3, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 1, 5, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 5, 1, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 1, 3, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 5, 3, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 3, 1, 5, 2], [1, 1, 0, 0]]} "Class ", 3546, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 5, 3, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 1, 5, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 5, 1, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 1, 3, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 5, 3, 2], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 3, 1, 5, 2], [0, 0, 1, 0]]} "Class ", 3547, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 5, 3, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 1, 5, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 5, 1, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 1, 3, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 5, 3, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 3, 1, 5, 2], [1, 0, 1, 0]]} "Class ", 3548, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 5, 3, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 1, 5, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 5, 1, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 1, 3, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 5, 3, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 3, 1, 5, 2], [0, 1, 1, 0]]} "Class ", 3549, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 5, 3, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 1, 5, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 5, 1, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 1, 3, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 5, 3, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 3, 1, 5, 2], [1, 1, 1, 0]]} "Class ", 3550, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 5, 3, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 1, 5, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 5, 1, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 1, 3, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 5, 3, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 3, 1, 5, 2], [0, 1, 0, 1]]} "Class ", 3551, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 5, 3, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 1, 5, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 5, 1, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 1, 3, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 5, 3, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 3, 1, 5, 2], [1, 1, 0, 1]]} "Class ", 3552, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 5, 3, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 1, 5, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 5, 1, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 1, 3, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 5, 3, 2], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 3, 1, 5, 2], [0, 0, 1, 1]]} "Class ", 3553, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 5, 3, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 1, 5, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 5, 1, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 1, 3, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 5, 3, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 3, 1, 5, 2], [1, 0, 1, 1]]} "Class ", 3554, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 5, 3, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 1, 5, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 5, 1, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 1, 3, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 5, 3, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 3, 1, 5, 2], [0, 1, 1, 1]]} "Class ", 3555, " is:" {{[[1, 3, 2], [0, 0]], [[4, 1, 5, 3, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 1, 5, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 5, 1, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 5, 1, 3, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 1, 5, 3, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 3, 1, 5, 2], [1, 1, 1, 1]]} "Class ", 3556, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 1, 3, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 4, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 5, 3, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 1, 3, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 2, 1, 3, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 4, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 5, 3, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 2, 1, 3, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}], [[4, 2, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 3, 4], {1, 2, 3}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 288, 1558, 9647, 67246, 520883, 4438391, 41255425, 415420394, 4504822572, 52339590151, 648652641551, 8541288515631, 119085320745668, 1752565158491044, 27149791314105680] "" "Class ", 3557, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 1, 3, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 5, 3, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 1, 3, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 2, 1, 3, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 5, 3, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 2, 1, 3, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 286, 1533, 9385, 64555, 492746, 4132408, 37764405, 373518995, 3975293507, 45297100524, 550197800931, 7096476455557, 96863762362534, 1394933966229289, 21136516322486356] "" "Class ", 3558, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 1, 3, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 4, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 2, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 5, 3, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 1, 3, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 5, 4, 2], [0, 1, 0, 0]]} "Class ", 3559, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 1, 3, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 4, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 2, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 5, 3, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 1, 3, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 5, 4, 2], [1, 1, 0, 0]]} "Class ", 3560, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 1, 3, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 4, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 2, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 5, 3, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 1, 3, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 5, 4, 2], [0, 0, 1, 0]]} "Class ", 3561, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 1, 3, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 5, 3, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 1, 3, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 1, 0]]} "Class ", 3562, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 1, 3, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 4, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 2, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 5, 3, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 1, 3, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 5, 4, 2], [0, 1, 1, 0]]} "Class ", 3563, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 1, 3, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 4, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 2, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 5, 3, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 1, 3, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 5, 4, 2], [1, 1, 1, 0]]} "Class ", 3564, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 1, 3, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 4, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 1, 3, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 5, 4, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 2, 1, 3, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 4, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 3, 5, 4, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 285, 1517, 9181, 62236, 466846, 3838323, 34318851, 331508772, 3440375787, 38174097950, 450974880662, 5651234392190, 74870220776875, 1045609545728458, 15352310587285071] "" "Class ", 3565, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 1, 3, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 1, 3, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 2, 1, 3, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1}, {[0, 1, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 283, 1488, 8852, 58710, 429157, 3426132, 29651480, 276483211, 2763142252, 29463748354, 333894870905, 4007344266444, 50778868436259, 677459506350089, 9492285604140301] "" "Class ", 3566, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 1, 3, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 4, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 2, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 1, 3, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 5, 4, 2], [0, 1, 0, 1]]} "Class ", 3567, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 1, 3, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 4, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 2, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 1, 3, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 5, 4, 2], [1, 1, 0, 1]]} "Class ", 3568, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 1, 3, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 4, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 2, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 5, 3, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 1, 3, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 5, 4, 2], [0, 0, 1, 1]]} "Class ", 3569, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 1, 3, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 5, 3, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 1, 3, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 1, 1]]} "Class ", 3570, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 1, 3, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 4, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 2, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 5, 3, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 1, 3, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 3, 5, 4, 2], [0, 1, 1, 1]]} "Class ", 3571, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 1, 3, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 3, 5, 4, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 3, 1, 2, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 5, 3, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 1, 3, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 3, 5, 4, 2], [1, 1, 1, 1]]} "Class ", 3572, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 1, 5, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 5, 4, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 1, 2, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 5, 1, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 1, 5, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 2, 1, 5, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 5, 4, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 1, 2, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 5, 1, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 2, 1, 5, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {[0, 0, 1, 0, 0]}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 294, 1596, 9888, 68827, 531865, 4517640, 41834003, 419443626, 4526867019, 52324861912, 644900397143, 8442474503256, 116990145621479, 1710808652759680, 26328874653706646] "" "Class ", 3573, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 1, 5, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 5, 4, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 1, 2, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 5, 1, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 1, 5, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 1, 5, 4, 2], [0, 1, 0, 0]]} "Class ", 3574, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 1, 5, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 5, 4, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 1, 2, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 5, 1, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 1, 5, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 1, 5, 4, 2], [1, 1, 0, 0]]} "Class ", 3575, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 1, 5, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 5, 4, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 1, 2, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 5, 1, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 1, 5, 3], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 1, 5, 4, 2], [1, 0, 1, 0]]} "Class ", 3576, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 1, 5, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 5, 4, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 1, 2, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 5, 1, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 1, 5, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 1, 5, 4, 2], [0, 1, 1, 0]]} "Class ", 3577, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 1, 5, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 5, 4, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 1, 2, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 5, 1, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 1, 5, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 1, 5, 4, 2], [1, 1, 1, 0]]} "Class ", 3578, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 1, 5, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 5, 4, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 1, 2, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 5, 1, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 1, 5, 3], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 1, 5, 4, 2], [1, 0, 0, 1]]} "Class ", 3579, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 1, 5, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 5, 4, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 1, 2, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 5, 1, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 1, 5, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 1, 5, 4, 2], [0, 1, 0, 1]]} "Class ", 3580, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 1, 5, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 5, 4, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 1, 2, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 5, 1, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 1, 5, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 1, 5, 4, 2], [1, 1, 0, 1]]} "Class ", 3581, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 1, 5, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 5, 4, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 1, 2, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 5, 1, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 1, 5, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 1, 5, 4, 2], [1, 0, 1, 1]]} "Class ", 3582, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 1, 5, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 5, 4, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 1, 2, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 5, 1, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 1, 5, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 1, 5, 4, 2], [0, 1, 1, 1]]} "Class ", 3583, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 1, 5, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 5, 4, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 5, 1, 2, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 5, 1, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 1, 5, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 1, 5, 4, 2], [1, 1, 1, 1]]} "Class ", 3584, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 3, 4, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 3, 2, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 5, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 3, 1, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 3, 4, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 3, 2, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 5, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 2, 3, 1, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {}], [[4, 2, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3}, {}], [[5, 2, 4, 1, 3], {1, 2}, {}], [[5, 3, 4, 1, 2], {1, 2}, {}], [[5, 3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 290, 1581, 9858, 69159, 539087, 4622421, 43238706, 438163254, 4781721238, 55910812876, 697326049862, 9240701787707, 129657489054593, 1920309994689025, 29937909962400125] "" "Class ", 3585, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 5, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 3, 1, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 5, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 2, 3, 1, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 286, 1537, 9410, 64655, 492693, 4122659, 37574732, 370512557, 3929925502, 44614170687, 539738383470, 6931973149117, 94193910306882, 1350109680343817, 20357164873198530] "" "Class ", 3586, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 1, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 3, 4, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 3, 2, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 5, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 3, 1, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 3, 4, 2], [0, 1, 0, 0]]} "Class ", 3587, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 1, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 3, 4, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 3, 2, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 5, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 3, 1, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 3, 4, 2], [1, 1, 0, 0]]} "Class ", 3588, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 1, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 3, 4, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 3, 2, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 5, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 3, 1, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 3, 4, 2], [0, 0, 1, 0]]} "Class ", 3589, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 1, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 5, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 3, 1, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 1, 0]]} "Class ", 3590, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 1, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 3, 4, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 3, 2, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 5, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 3, 1, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 3, 4, 2], [0, 1, 1, 0]]} "Class ", 3591, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 1, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 3, 4, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 3, 2, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 5, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 3, 1, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 3, 4, 2], [1, 1, 1, 0]]} "Class ", 3592, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 1, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 3, 4, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 3, 2, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 3, 1, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 3, 4, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 1, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 3, 4, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 3, 2, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 5, 3, 4, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 286, 1534, 9384, 64421, 490243, 4095617, 37262114, 366717652, 3881680408, 43972024122, 530789931388, 6801520002085, 92206413270360, 1318499163397137, 19832936464988772] "" "Class ", 3593, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 1, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 3, 1, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 1, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 282, 1473, 8654, 56264, 399950, 3079611, 25494716, 225518995, 2120491416, 21100234542, 221349577730, 2439877207353, 28176473477998, 340024680915781, 4277952067939418] "" "Class ", 3594, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 1, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 3, 4, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 3, 2, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 3, 1, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 3, 4, 2], [0, 1, 0, 1]]} "Class ", 3595, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 1, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 3, 4, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 3, 2, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 3, 1, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 3, 4, 2], [1, 1, 0, 1]]} "Class ", 3596, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 1, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 3, 4, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 3, 2, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 5, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 3, 1, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 3, 4, 2], [0, 0, 1, 1]]} "Class ", 3597, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 1, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 5, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 3, 1, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 1, 1]]} "Class ", 3598, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 1, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 3, 4, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 3, 2, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 5, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 3, 1, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 3, 4, 2], [0, 1, 1, 1]]} "Class ", 3599, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 1, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 3, 4, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 3, 2, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 5, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 3, 1, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 3, 4, 2], [1, 1, 1, 1]]} "Class ", 3600, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 3, 4, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 3, 2, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 1, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 3, 5, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 3, 4, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 3, 2, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 1, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 2, 3, 5, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {}, {}], [[4, 1, 2, 3], {1, 2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}], [[3, 1, 2, 4, 5], {1, 2, 3}, {}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 3, 5, 2], {1, 2, 3}, {}], [[4, 2, 3, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 286, 1548, 9600, 66969, 518894, 4422043, 41111104, 414062504, 4491187554, 52193917627, 647003378296, 8521613500893, 118839472611164, 1749366292221371, 27106734841766592] "" "Class ", 3601, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 1, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 3, 5, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 1, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 2, 3, 5, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2}, {[1, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1515, 9226, 63091, 478465, 3984065, 36131236, 354479221, 3740685677, 42247700588, 508464169626, 6496275762939, 87810371129085, 1251967811172375, 18777123973055098] "" "Class ", 3602, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 5, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 3, 4, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 3, 2, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 1, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 3, 5, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 3, 4, 2], [0, 1, 0, 0]]} "Class ", 3603, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 5, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 3, 4, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 3, 2, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 1, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 3, 5, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 3, 4, 2], [1, 1, 0, 0]]} "Class ", 3604, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 5, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 3, 4, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 3, 2, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 1, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 3, 5, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 3, 4, 2], [0, 0, 1, 0]]} "Class ", 3605, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 5, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 1, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 3, 5, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 1, 0]]} "Class ", 3606, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 5, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 3, 4, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 3, 2, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 1, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 3, 5, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 3, 4, 2], [0, 1, 1, 0]]} "Class ", 3607, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 5, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 3, 4, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 3, 2, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 1, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 3, 5, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 3, 4, 2], [1, 1, 1, 0]]} "Class ", 3608, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 5, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 3, 4, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 3, 2, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 1, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 3, 5, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 3, 4, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 5, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 3, 4, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 3, 2, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 1, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[5, 1, 3, 4, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 282, 1483, 8870, 59439, 440708, 3580055, 31616592, 301591668, 3090314074, 33851270035, 394734727760, 4881823944570, 63822855627502, 879451336453937, 12739192446538186] "" "Class ", 3609, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 5, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 1, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 3, 5, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 5, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 1, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2, 3}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {2}, {}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 280, 1442, 8313, 52890, 367338, 2760832, 22297125, 192383866, 1764698026, 17136856578, 175537035056, 1890588356028, 21349633397532, 252149248226421, 3107564399374613] "" "Class ", 3610, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 5, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 3, 4, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 3, 2, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 1, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 3, 5, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 3, 4, 2], [0, 1, 0, 1]]} "Class ", 3611, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 5, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 3, 4, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 3, 2, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 1, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 3, 5, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 3, 4, 2], [1, 1, 0, 1]]} "Class ", 3612, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 5, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 3, 4, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 3, 2, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 1, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 3, 5, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 3, 4, 2], [0, 0, 1, 1]]} "Class ", 3613, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 5, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 1, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 3, 5, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 1, 1]]} "Class ", 3614, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 5, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 3, 4, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 3, 2, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 1, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 3, 5, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 3, 4, 2], [0, 1, 1, 1]]} "Class ", 3615, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 5, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 3, 4, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 3, 2, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 3, 1, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 3, 5, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 3, 4, 2], [1, 1, 1, 1]]} "Class ", 3616, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 1, 4, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 5, 2, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 1, 5, 3], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 1, 4, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 5, 2, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 1, 5, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {}], [[3, 2, 4, 1, 5], {1, 2}, {}], [[3, 2, 5, 1, 4], {1, 2, 3}, {}], [[4, 2, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 1, 2], {1, 2, 3}, {}], [[4, 3, 5, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 288, 1562, 9687, 67617, 524524, 4475632, 41660220, 420094727, 4561993291, 53079280535, 658756212878, 8686673527888, 121284668190019, 1787472774200922, 27729966592767230] "" "Class ", 3617, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 1, 4, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 5, 2, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 1, 5, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 1, 4, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 5, 2, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 1, 5, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 286, 1536, 9400, 64581, 492269, 4122349, 37621046, 371630008, 3950548807, 44966964724, 545657869231, 7031799175769, 95906941367307, 1380220870003142, 20901343318167615] "" "Class ", 3618, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 5, 1, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 1, 4, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 5, 2, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 1, 5, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 5, 1, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 5, 1, 4, 2], [0, 1, 0, 0]]} "Class ", 3619, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 5, 1, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 1, 4, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 5, 2, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 1, 5, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 5, 1, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 5, 1, 4, 2], [1, 1, 0, 0]]} "Class ", 3620, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 5, 1, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 1, 4, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 5, 2, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 1, 5, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 5, 1, 3], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[3, 5, 1, 4, 2], [0, 0, 1, 0]]} "Class ", 3621, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 5, 1, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 1, 4, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 5, 2, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 1, 5, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 5, 1, 3], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 5, 1, 4, 2], [1, 0, 1, 0]]} "Class ", 3622, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 5, 1, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 1, 4, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 5, 2, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 1, 5, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 5, 1, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 5, 1, 4, 2], [0, 1, 1, 0]]} "Class ", 3623, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 5, 1, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 1, 4, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 5, 2, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 1, 5, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 5, 1, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 5, 1, 4, 2], [1, 1, 1, 0]]} "Class ", 3624, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 5, 1, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 1, 4, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 5, 2, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 1, 5, 3], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 5, 1, 3], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[3, 5, 1, 4, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 2, 5, 1, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 1, 4, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 5, 2, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 1, 5, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[3, 5, 1, 4, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1508, 9114, 61739, 463197, 3812345, 34152643, 330815945, 3445278015, 38389749636, 455726129947, 5741888367114, 76527201804557, 1075696249325554, 15904117236070239] "" "Class ", 3625, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 5, 1, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 1, 4, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 5, 2, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 1, 5, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 5, 1, 3], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 5, 1, 4, 2], [1, 0, 0, 1]]} "Class ", 3626, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 5, 1, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 1, 4, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 5, 2, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 1, 5, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 5, 1, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 5, 1, 4, 2], [0, 1, 0, 1]]} "Class ", 3627, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 5, 1, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 1, 4, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 5, 2, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 1, 5, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 5, 1, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 5, 1, 4, 2], [1, 1, 0, 1]]} "Class ", 3628, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 5, 1, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 1, 4, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 5, 2, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 1, 5, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 5, 1, 3], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[3, 5, 1, 4, 2], [0, 0, 1, 1]]} "Class ", 3629, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 5, 1, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 1, 4, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 5, 2, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 1, 5, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 5, 1, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 5, 1, 4, 2], [1, 0, 1, 1]]} "Class ", 3630, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 5, 1, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 1, 4, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 5, 2, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 1, 5, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 5, 1, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 5, 1, 4, 2], [0, 1, 1, 1]]} "Class ", 3631, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 5, 1, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 1, 4, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 5, 2, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 1, 5, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 5, 1, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 5, 1, 4, 2], [1, 1, 1, 1]]} "Class ", 3632, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 5, 3, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 1, 4, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 5, 2, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 1, 3, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 5, 3, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 3, 1, 4, 2], [0, 1, 0, 0]]} "Class ", 3633, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 5, 3, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 1, 4, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 5, 2, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 1, 3, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 5, 3, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 3, 1, 4, 2], [1, 1, 0, 0]]} "Class ", 3634, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 5, 3, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 1, 4, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 5, 2, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 1, 3, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 5, 3, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 3, 1, 4, 2], [0, 0, 1, 0]]} "Class ", 3635, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 5, 3, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 1, 3, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 5, 3, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 1, 0]]} "Class ", 3636, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 5, 3, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 1, 4, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 5, 2, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 1, 3, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 5, 3, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 3, 1, 4, 2], [0, 1, 1, 0]]} "Class ", 3637, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 5, 3, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 1, 4, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 5, 2, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 1, 3, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 5, 3, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 3, 1, 4, 2], [1, 1, 1, 0]]} "Class ", 3638, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 5, 3, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 1, 4, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 5, 2, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 1, 3, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 5, 3, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 3, 1, 4, 2], [0, 1, 0, 1]]} "Class ", 3639, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 5, 3, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 1, 4, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 5, 2, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 1, 3, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 5, 3, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 3, 1, 4, 2], [1, 1, 0, 1]]} "Class ", 3640, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 5, 3, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 1, 4, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 5, 2, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 1, 3, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 5, 3, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 3, 1, 4, 2], [0, 0, 1, 1]]} "Class ", 3641, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 5, 3, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 1, 3, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 5, 3, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 1, 1]]} "Class ", 3642, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 5, 3, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 1, 4, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 5, 2, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 1, 3, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 5, 3, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 3, 1, 4, 2], [0, 1, 1, 1]]} "Class ", 3643, " is:" {{[[1, 3, 2], [0, 0]], [[4, 2, 5, 3, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 1, 4, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 5, 2, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 4, 1, 3, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 2, 5, 3, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 3, 1, 4, 2], [1, 1, 1, 1]]} "Class ", 3644, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 2, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 5, 4, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 1, 2, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 2, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 5, 4, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 3, 1, 2, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {1}, {}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3}, {}], [[5, 4, 1, 2, 3], {1, 2, 3}, {}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 290, 1580, 9854, 69168, 539443, 4627839, 43310557, 439104219, 4794315795, 56085300828, 699842331393, 9278555382234, 130251908803713, 1930051585582698, 30104410885147204] "" "Class ", 3645, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 2, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 5, 4, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 1, 2, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 2, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 5, 4, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 3, 1, 2, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 287, 1547, 9531, 66036, 508011, 4296224, 39612887, 395477752, 4250027346, 48914974804, 600279971725, 7824249390981, 107948312824241, 1571601310524066, 24078409897637776] "" "Class ", 3646, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 2, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 3, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 3, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 5, 4, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 1, 2, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 5, 3, 2], [0, 1, 0, 0]]} "Class ", 3647, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 2, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 3, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 3, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 5, 4, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 1, 2, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 4, 5, 3, 2], [1, 1, 0, 0]]} "Class ", 3648, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 2, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 3, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 3, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 5, 4, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 1, 2, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 5, 3, 2], [0, 0, 1, 0]]} "Class ", 3649, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 2, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 5, 4, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 1, 2, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 1, 0]]} "Class ", 3650, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 2, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 3, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 3, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 5, 4, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 1, 2, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 5, 3, 2], [0, 1, 1, 0]]} "Class ", 3651, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 2, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 3, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 3, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 5, 4, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 1, 2, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 4, 5, 3, 2], [1, 1, 1, 0]]} "Class ", 3652, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 2, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 3, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 3, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 5, 4, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 1, 2, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 5, 3, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 2, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 3, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 3, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 5, 4, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 4, 5, 3, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 287, 1542, 9442, 64867, 493769, 4124568, 37508974, 368885301, 3900959116, 44140344325, 532128659311, 6808791842500, 92159003306280, 1315581044887008, 19753292357755052] "" "Class ", 3653, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 2, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 5, 4, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 1, 2, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 2, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 5, 4, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1502, 8993, 59995, 440536, 3526631, 30543560, 284381319, 2831211640, 30000944202, 337021222621, 3999671386007, 49991798473392, 656282369069683, 9026809352274482] "" "Class ", 3654, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 2, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 3, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 3, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 5, 4, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 1, 2, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 5, 3, 2], [0, 1, 0, 1]]} "Class ", 3655, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 2, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 3, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 3, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 5, 4, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 1, 2, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 4, 5, 3, 2], [1, 1, 0, 1]]} "Class ", 3656, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 2, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 3, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 3, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 5, 4, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 1, 2, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 5, 3, 2], [0, 0, 1, 1]]} "Class ", 3657, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 2, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 5, 4, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 1, 2, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 1, 1]]} "Class ", 3658, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 2, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 3, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 3, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 5, 4, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 1, 2, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 4, 5, 3, 2], [0, 1, 1, 1]]} "Class ", 3659, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 2, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 4, 5, 3, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 2, 1, 3, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 5, 4, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 1, 2, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 4, 5, 3, 2], [1, 1, 1, 1]]} "Class ", 3660, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 5, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 5, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 1, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 5, 1, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 1, 5, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 5, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 5, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 1, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 5, 1, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 3, 1, 5, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 294, 1598, 9922, 69245, 536654, 4572245, 42469848, 427118956, 4623559247, 53599657849, 662506954953, 8697178231174, 120846754399905, 1771865270529838, 27338341186960644] "" "Class ", 3661, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 5, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 5, 3, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 1, 3, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 5, 1, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 1, 5, 2], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 1, 5, 3, 2], [0, 1, 0, 0]]} "Class ", 3662, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 5, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 5, 3, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 1, 3, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 5, 1, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 1, 5, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 5, 3, 2], [1, 1, 0, 0]]} "Class ", 3663, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 5, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 5, 3, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 1, 3, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 5, 1, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 1, 5, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 5, 3, 2], [1, 0, 1, 0]]} "Class ", 3664, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 5, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 5, 3, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 1, 3, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 5, 1, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 1, 5, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 1, 5, 3, 2], [0, 1, 1, 0]]} "Class ", 3665, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 5, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 5, 3, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 1, 3, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 5, 1, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 1, 5, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 5, 3, 2], [1, 1, 1, 0]]} "Class ", 3666, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 5, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 5, 3, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 1, 3, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 5, 1, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 1, 5, 2], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 5, 3, 2], [1, 0, 0, 1]]} "Class ", 3667, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 5, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 5, 3, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 1, 3, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 5, 1, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 1, 5, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 1, 5, 3, 2], [0, 1, 0, 1]]} "Class ", 3668, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 5, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 5, 3, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 1, 3, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 5, 1, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 1, 5, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 5, 3, 2], [1, 1, 0, 1]]} "Class ", 3669, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 5, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 5, 3, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 1, 3, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 5, 1, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 1, 5, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 5, 3, 2], [1, 0, 1, 1]]} "Class ", 3670, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 5, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 5, 3, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 1, 3, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 5, 1, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 1, 5, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 1, 5, 3, 2], [0, 1, 1, 1]]} "Class ", 3671, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 5, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 1, 5, 3, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 5, 1, 3, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 5, 1, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 1, 5, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 1, 5, 3, 2], [1, 1, 1, 1]]} "Class ", 3672, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {}, {}], [[4, 3, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 2, 3}, {}], [[5, 4, 2, 1, 3], {1, 2, 3}, {}], [[5, 4, 3, 1, 2], {1, 2, 3}, {}], [[5, 4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 291, 1590, 9933, 69821, 545311, 4685001, 43910550, 445850807, 4875228472, 57116756632, 713773917252, 9477346041072, 133240538186248, 1977275153087083, 30886893915002310] "" "Class ", 3673, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 288, 1559, 9631, 66931, 516595, 4383760, 40564613, 406476605, 4384790061, 50661888716, 624182946536, 8168683746998, 113163626311702, 1654408801568357, 25454429330587339] "" "Class ", 3674, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 1, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 3, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 3, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 5, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 2, 1, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 4, 3, 2], [0, 1, 0, 0]]} "Class ", 3675, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 3, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 5, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 4, 3, 2], [1, 1, 0, 0]]} "Class ", 3676, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 1, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 3, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 3, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 5, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 2, 1, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 4, 3, 2], [0, 0, 1, 0]]} "Class ", 3677, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 1, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 5, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 2, 1, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 1, 0]]} "Class ", 3678, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 1, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 3, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 3, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 5, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 2, 1, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 4, 3, 2], [0, 1, 1, 0]]} "Class ", 3679, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 1, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 3, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 3, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 5, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 2, 1, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 4, 3, 2], [1, 1, 1, 0]]} "Class ", 3680, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 289, 1568, 9716, 67670, 523236, 4447140, 41208828, 413456650, 4465310065, 51648528409, 636992522102, 8344451485830, 115706374797497, 1693099877422149, 26072312478838743] "" "Class ", 3681, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 286, 1531, 9315, 63470, 478342, 3948614, 35420318, 342980138, 3564906199, 39580994790, 467470620911, 5851202155913, 77363719169803, 1077366383536041, 15761080537929240] "" "Class ", 3682, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 1, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 3, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 3, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 5, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 2, 1, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 4, 3, 2], [0, 1, 0, 1]]} "Class ", 3683, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 1, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 5, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 2, 1, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]} "Class ", 3684, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 1, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 3, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 3, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 5, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 2, 1, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 4, 3, 2], [0, 0, 1, 1]]} "Class ", 3685, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 1, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 5, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 2, 1, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 1, 1]]} "Class ", 3686, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 1, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 3, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 3, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 5, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 2, 1, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[1, 5, 4, 3, 2], [0, 1, 1, 1]]} "Class ", 3687, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 5, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]} "Class ", 3688, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 1, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 1, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}], [[3, 2, 1, 4, 5], {1, 2, 3}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 287, 1562, 9732, 68177, 530555, 4541129, 42402535, 428940792, 4672925507, 54543414224, 679084673184, 8983266870814, 125825411885983, 1860302529827274, 28951774292370796] "" "Class ", 3689, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 1, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 1, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {[1, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 286, 1547, 9571, 66552, 513912, 4362970, 40389125, 404893779, 4369654263, 50509770582, 622594714387, 8151711579896, 112982292456430, 1652557845306380, 25438463407297288] "" "Class ", 3690, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 5, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 3, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 3, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 1, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 2, 5, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 4, 3, 2], [0, 1, 0, 0]]} "Class ", 3691, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 5, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 3, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 3, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 1, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 2, 5, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 4, 3, 2], [1, 1, 0, 0]]} "Class ", 3692, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 5, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 3, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 3, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 1, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 2, 5, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 4, 3, 2], [0, 0, 1, 0]]} "Class ", 3693, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 5, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 1, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 2, 5, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 1, 0]]} "Class ", 3694, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 5, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 3, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 3, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 1, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 2, 5, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 4, 3, 2], [0, 1, 1, 0]]} "Class ", 3695, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 5, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 3, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 3, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 1, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 2, 5, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 4, 3, 2], [1, 1, 1, 0]]} "Class ", 3696, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 3, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 3, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 1, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 4, 3, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 3, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 3, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 1, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[5, 1, 4, 3, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {}], [[4, 1, 2, 3], {1, 2, 3}, {}], [[4, 1, 3, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 285, 1531, 9399, 64791, 495282, 4158301, 38044020, 376717451, 4013871135, 45787843543, 556777324124, 7189367122469, 98242438486394, 1416403315208649, 21486650898668620] "" "Class ", 3697, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 1, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 1, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2, 3}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {2}, {[0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1513, 9170, 62166, 465690, 3817585, 33981008, 326274980, 3360382971, 36945451703, 431802468281, 5345254662535, 69855924039985, 961027127687229, 13881651460378172] "" "Class ", 3698, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 3, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 3, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 1, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 4, 3, 2], [0, 1, 0, 1]]} "Class ", 3699, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 3, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 3, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 1, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 4, 3, 2], [1, 1, 0, 1]]} "Class ", 3700, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 5, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 3, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 3, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 1, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 2, 5, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 4, 3, 2], [0, 0, 1, 1]]} "Class ", 3701, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 5, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 1, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 2, 5, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 1, 1]]} "Class ", 3702, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 5, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 3, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 3, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 1, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 2, 5, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 1, 4, 3, 2], [0, 1, 1, 1]]} "Class ", 3703, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 5, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 1, 4, 3, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 5, 2, 3, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 4, 1, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 2, 5, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 1, 4, 3, 2], [1, 1, 1, 1]]} "Class ", 3704, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 5, 4], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 5, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {}], [[3, 2, 4, 1, 5], {1, 2}, {}], [[3, 2, 5, 1, 4], {1, 2, 3}, {}], [[4, 2, 5, 1, 3], {1, 2, 3}, {}], [[4, 3, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 288, 1567, 9752, 68306, 531633, 4551054, 42499609, 429950678, 4684228924, 54679200958, 680824741828, 9006942588385, 126166185932246, 1865475783944178, 29034386009822202] "" "Class ", 3705, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 5, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 5, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 287, 1548, 9521, 65778, 504267, 4247229, 38982737, 387237230, 4138886425, 47359637842, 577630447317, 7480620728020, 102515862972486, 1482143326379570, 22544988294744000] "" "Class ", 3706, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 5, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 5, 4], [0, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {}, {}], [[3, 4, 1, 2, 5], {2, 3, 4}, {}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {2, 3, 4}, {}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3}, {}], [[4, 5, 3, 1, 2], {3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 285, 1527, 9344, 64253, 490152, 4105796, 37457660, 369654879, 3923147700, 44552636135, 539028999186, 6921205483999, 93995156339301, 1346068679162248, 20271527358136104] "" "Class ", 3707, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 3, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 3, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 5, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 5, 1, 3, 2], [1, 1, 0, 0]]} "Class ", 3708, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 3, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 5, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 0, 1, 0]]} "Class ", 3709, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 3, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 3, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 5, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 5, 1, 3, 2], [1, 0, 1, 0]]} "Class ", 3710, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 5, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 1, 0]]} "Class ", 3711, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 3, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 3, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 5, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 5, 1, 3, 2], [1, 1, 1, 0]]} "Class ", 3712, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 3, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 5, 4], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 3, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 5, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1506, 9071, 61167, 456262, 3729574, 33150699, 318335419, 3284169570, 36226157489, 425449701967, 5300208321981, 69811384347060, 969326137774657, 14150579142475773] "" "Class ", 3713, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 3, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 3, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 5, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 5, 1, 3, 2], [1, 0, 0, 1]]} "Class ", 3714, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {}], [[3, 4, 1, 2, 5], {2, 3, 4}, {[0, 1, 0, 0, 0, 0]}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {2, 3, 4}, {[0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3}, {[0, 0, 1, 0, 0, 0]}], [[4, 5, 3, 1, 2], {3}, {[0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 281, 1455, 8433, 53885, 375234, 2822024, 22757723, 195634785, 1783877691, 17181324607, 174157736347, 1852033290898, 20604695195427, 239234603693951, 2892452639702486] "" "Class ", 3715, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 3, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 3, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 5, 1, 3, 2], [1, 1, 0, 1]]} "Class ", 3716, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 3, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 5, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 0, 1, 1]]} "Class ", 3717, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 3, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 3, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 5, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 5, 1, 3, 2], [1, 0, 1, 1]]} "Class ", 3718, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 5, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 1, 1]]} "Class ", 3719, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 1, 3, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 5, 3, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 5, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 5, 1, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 5, 1, 3, 2], [1, 1, 1, 1]]} "Class ", 3720, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {}], [[3, 2, 4, 1, 5], {1, 2}, {}], [[3, 2, 5, 1, 4], {1, 2, 3}, {}], [[4, 2, 5, 1, 3], {1, 2, 3}, {}], [[4, 3, 5, 1, 2], {1, 2, 3}, {}], [[4, 3, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 287, 1562, 9735, 68215, 530891, 4544326, 42436753, 429335128, 4677743154, 54605571866, 679931617402, 8995440886340, 126009556656266, 1863226639821764, 29000418289892382] "" "Class ", 3721, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 283, 1510, 9252, 63767, 487378, 4091618, 37438682, 370851622, 3953412824, 45126111150, 549107422596, 7095562461156, 97035956818771, 1400135412515518, 21257370995020139] "" "Class ", 3722, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 2, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 5, 2, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 0]]} "Class ", 3723, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 2, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 3, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 3, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 5, 2, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 4, 1, 3, 2], [1, 1, 0, 0]]} "Class ", 3724, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 2, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 3, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 4, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 5, 2, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 0, 1, 0]]} "Class ", 3725, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 2, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 4, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 5, 2, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 1, 0]]} "Class ", 3726, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 2, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 4, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 5, 2, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 1, 0]]} "Class ", 3727, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 2, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 3, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 3, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 4, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 5, 2, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 4, 1, 3, 2], [1, 1, 1, 0]]} "Class ", 3728, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 3, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 3, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 283, 1496, 8977, 60243, 446896, 3629585, 32029675, 305131817, 3120711558, 34102330970, 396522040067, 4887752146169, 63664388085952, 873706876716006, 12600304302785632] "" "Class ", 3729, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2, 3}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {2}, {}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 279, 1428, 8175, 51581, 354534, 2630684, 20924059, 177365830, 1594436791, 15136821449, 151209821734, 1584422648325, 17365982116195, 198606425057355, 2364807551475130] "" "Class ", 3730, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]} "Class ", 3731, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 3, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]} "Class ", 3732, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 2, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 3, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 4, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 5, 2, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 0, 1, 1]]} "Class ", 3733, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 2, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 4, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 5, 2, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 1, 1]]} "Class ", 3734, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 2, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 4, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 5, 2, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]} "Class ", 3735, " is:" {{[[1, 3, 2], [0, 0]], [[4, 3, 5, 2, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 1, 3, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 5, 3, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 3, 1, 4, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 3, 5, 2, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 4, 1, 3, 2], [1, 1, 1, 1]]} "Class ", 3736, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 5, 4, 3], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 5, 4, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[3, 4, 1, 2, 5], {1, 2, 3}, {}], [[3, 5, 1, 2, 4], {1, 2, 3}, {}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 285, 1525, 9320, 64071, 489460, 4112931, 37702472, 374416403, 4004267768, 45883330589, 560810480212, 7282927395633, 100142732227860, 1453496613690837, 22206748226533756] "" "Class ", 3737, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 5, 4, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 5, 4, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1504, 9036, 60719, 451161, 3672957, 32515443, 310997166, 3196089023, 35123159746, 411013122699, 5102642807767, 66985451217445, 927109735085919, 13492574924246621] "" "Class ", 3738, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 1, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 5, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 5, 4, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 4, 5, 1, 2], [0, 1, 0, 0]]} "Class ", 3739, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 1, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 5, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 5, 4, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 4, 5, 1, 2], [1, 1, 0, 0]]} "Class ", 3740, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2, 3}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {3}, {}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 2, 4], {3}, {}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {2, 3}, {}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 282, 1472, 8656, 56538, 405794, 3172568, 26826142, 243863460, 2371071032, 24548243446, 269577362768, 3129259444124, 38279805455072, 492133261851880, 6633067032622296] "" "Class ", 3741, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {[0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2, 3}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 2, 4], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {2, 3}, {}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3, 4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 281, 1451, 8359, 52895, 363468, 2688353, 21256684, 178682664, 1589417962, 14902413999, 146779744882, 1514200112208, 16318445934514, 183295070443488, 2141429479876715] "" "Class ", 3742, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 1, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 5, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 4, 5, 1, 2], [0, 1, 1, 0]]} "Class ", 3743, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 1, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 5, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 5, 4, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 4, 5, 1, 2], [1, 1, 1, 0]]} "Class ", 3744, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 5, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 5, 4, 3], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 5, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 5, 4, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 283, 1494, 8947, 59949, 444392, 3610038, 31894415, 304467729, 3123009415, 34255050585, 400095770400, 4957700294254, 64959316042685, 897359370990382, 13034761517878452] "" "Class ", 3745, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 5, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 5, 4, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 0, 1]]} "Class ", 3746, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 1, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 5, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 5, 4, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 4, 5, 1, 2], [0, 1, 0, 1]]} "Class ", 3747, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 1, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 5, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 5, 4, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 4, 5, 1, 2], [1, 1, 0, 1]]} "Class ", 3748, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 1, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 5, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 5, 4, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[3, 4, 5, 1, 2], [0, 0, 1, 1]]} "Class ", 3749, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 5, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 5, 4, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 1]]} "Class ", 3750, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 1, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 5, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 5, 4, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 4, 5, 1, 2], [0, 1, 1, 1]]} "Class ", 3751, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 1, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 5, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 5, 4, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 1, 2, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 4, 5, 1, 2], [1, 1, 1, 1]]} "Class ", 3752, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 1, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 5, 3, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 1, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 5, 3, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 292, 1558, 9425, 63764, 476915, 3906861, 34788495, 334571019, 3456216683, 38168295118, 448724799537, 5595419111129, 73762934498919, 1025001145052420, 14974283186072310] "" "Class ", 3753, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 1, 3, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 5, 1, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 1, 5, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 5, 3, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 1, 3, 2], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 3, 5, 1, 2], [0, 1, 0, 0]]} "Class ", 3754, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 1, 3, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 5, 1, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 1, 5, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 5, 3, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 1, 3, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 3, 5, 1, 2], [1, 1, 0, 0]]} "Class ", 3755, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2, 3}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 292, 1541, 9040, 57984, 401950, 2985445, 23600768, 197523759, 1742629372, 16147599715, 156669439886, 1587334971122, 16754730615350, 183858442369760, 2093613699130224] "" "Class ", 3756, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 5, 1, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 1, 5, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 3, 5, 1, 2], [0, 1, 1, 0]]} "Class ", 3757, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 5, 1, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 1, 5, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 5, 3, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 1, 3, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 3, 5, 1, 2], [1, 1, 1, 0]]} "Class ", 3758, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 1, 3, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 1, 5, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 5, 3, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 1, 3, 2], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 0, 1]]} "Class ", 3759, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 1, 3, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 5, 1, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 1, 5, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 5, 3, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 1, 3, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 3, 5, 1, 2], [0, 1, 0, 1]]} "Class ", 3760, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 1, 3, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 5, 1, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 1, 5, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 5, 3, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 1, 3, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 3, 5, 1, 2], [1, 1, 0, 1]]} "Class ", 3761, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 1, 3, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 5, 3, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 1, 3, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 1]]} "Class ", 3762, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 1, 3, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 5, 1, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 1, 5, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 5, 3, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 1, 3, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 3, 5, 1, 2], [0, 1, 1, 1]]} "Class ", 3763, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 1, 3, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 5, 1, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 1, 5, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 5, 3, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 1, 3, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 3, 5, 1, 2], [1, 1, 1, 1]]} "Class ", 3764, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 5, 3], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 5, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 286, 1539, 9460, 65418, 502764, 4250091, 39193510, 391561559, 4212752102, 48561808107, 597109311616, 7800837882445, 107907659592244, 1575594763720283, 24216595667807604] "" "Class ", 3765, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 5, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 5, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1506, 9049, 60729, 450137, 3650561, 32152715, 305617486, 3117956778, 33982715596, 394052472343, 4843715202986, 62911628650900, 860907239890595, 12380145642957241] "" "Class ", 3766, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 5, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 5, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 1, 0, 0]]} "Class ", 3767, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 1, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 5, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 5, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 5, 4, 1, 2], [1, 1, 0, 0]]} "Class ", 3768, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {}, {}], [[2, 3, 1, 4, 5], {1, 2, 3}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2, 3}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {3}, {}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 1, 5], {3}, {}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 2, 4], {3}, {}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {3}, {}], [[3, 5, 2, 4, 1], {2, 3}, {}], [[4, 5, 1, 2, 3], {3}, {}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3}, {}], [[4, 5, 3, 1, 2], {3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 283, 1494, 8949, 59936, 443796, 3598726, 31712612, 301736742, 3082646545, 33653950158, 390973531627, 4815646751795, 62680993747337, 859648129003469, 12389876835927243] "" "Class ", 3769, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2, 3}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {3}, {}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 2, 4], {3}, {}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {2, 3}, {}], [[4, 5, 1, 2, 3], {3}, {}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3, 4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 282, 1472, 8627, 55894, 395838, 3036802, 25063460, 221277120, 2079827837, 20727733477, 218265596537, 2420969113643, 28208516291060, 344430399095690, 4397458303428898] "" "Class ", 3770, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 5, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 1, 1, 0]]} "Class ", 3771, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 1, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 5, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 5, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 5, 4, 1, 2], [1, 1, 1, 0]]} "Class ", 3772, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 5, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 5, 3], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 5, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 5, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 285, 1525, 9300, 63696, 484143, 4042693, 36790818, 362426575, 3842152275, 43614755967, 527828899144, 6783917818045, 92281494070738, 1324559172840667, 20006102388242735] "" "Class ", 3773, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 5, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 5, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 0, 1]]} "Class ", 3774, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 5, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 5, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 1, 0, 1]]} "Class ", 3775, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 1, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 5, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 5, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 5, 4, 1, 2], [1, 1, 0, 1]]} "Class ", 3776, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 5, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 5, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 0, 1, 1]]} "Class ", 3777, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 5, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 5, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 5, 4, 1, 2], [1, 0, 1, 1]]} "Class ", 3778, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 5, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 5, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 5, 4, 1, 2], [0, 1, 1, 1]]} "Class ", 3779, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 1, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 5, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 5, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 2, 1, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 5, 4, 1, 2], [1, 1, 1, 1]]} "Class ", 3780, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 3, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 3, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[3, 4, 1, 2, 5], {1, 2, 3}, {}], [[3, 5, 1, 2, 4], {1, 2, 3}, {}], [[4, 5, 1, 2, 3], {1, 2, 3}, {}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1521, 9328, 64325, 492868, 4155162, 38214440, 380719423, 4084804788, 46957418729, 575789594400, 7501565131938, 103481831697236, 1506806351864753, 23095483073430680] "" "Class ", 3781, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 3, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 3, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {[1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 281, 1470, 8747, 58303, 430136, 3479896, 30634598, 291530842, 2982212216, 32633309810, 380368877030, 4704803959488, 61549523441692, 849105960334387, 12319436679078198] "" "Class ", 3782, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 1, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 5, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 3, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 3, 4, 1, 2], [0, 1, 0, 0]]} "Class ", 3783, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 1, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 5, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 3, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 3, 4, 1, 2], [1, 1, 0, 0]]} "Class ", 3784, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2, 3}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {3}, {}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 2, 4], {3}, {}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {2, 3}, {}], [[4, 5, 1, 2, 3], {3}, {}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 280, 1450, 8484, 55284, 396616, 3104788, 26329336, 240405888, 2351066904, 24514111592, 271434566656, 3180424798848, 39311552300800, 511160791509248, 6974381761314912] "" "Class ", 3785, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {[1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2, 3}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {3}, {[1, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 2, 4], {3}, {[1, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {2, 3}, {}], [[4, 5, 1, 2, 3], {3}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 278, 1409, 7942, 49123, 329830, 2383820, 18422606, 151419743, 1317652540, 12092533185, 116644446380, 1179114643248, 12458316861976, 137267004595637, 1573887881790816] "" "Class ", 3786, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 1, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 5, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 3, 4, 1, 2], [0, 1, 1, 0]]} "Class ", 3787, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 1, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 5, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 3, 4, 1, 2], [1, 1, 1, 0]]} "Class ", 3788, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 5, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 3, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 5, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 3, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {}], [[4, 1, 2, 3], {1, 2, 3}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 283, 1504, 9128, 62173, 469773, 3900141, 35281282, 345397567, 3638446559, 41034986077, 493323763965, 6297741351723, 85081528514465, 1212726536054341, 18187902922075072] "" "Class ", 3789, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 3, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 3, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2, 3}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {2}, {}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2}, {[0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 280, 1450, 8481, 55195, 395022, 3080982, 25995663, 235811376, 2287666533, 23627491113, 258779237301, 2995212677195, 36524525627936, 467968438223997, 6284366020987608] "" "Class ", 3790, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 1, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 5, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 3, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 3, 4, 1, 2], [0, 1, 0, 1]]} "Class ", 3791, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 1, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 5, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 3, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 3, 4, 1, 2], [1, 1, 0, 1]]} "Class ", 3792, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 5, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 3, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]} "Class ", 3793, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 3, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]} "Class ", 3794, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 1, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 5, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 3, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 3, 4, 1, 2], [0, 1, 1, 1]]} "Class ", 3795, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 1, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 5, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 4, 3, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 2, 3, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 3, 4, 1, 2], [1, 1, 1, 1]]} "Class ", 3796, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 5, 4], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 5, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 285, 1529, 9376, 64667, 495688, 4179615, 38444117, 383081308, 4110910806, 47265694563, 579673445054, 7553531075822, 104217336045703, 1517787783404911, 23267974139806978] "" "Class ", 3797, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 5, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 5, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1506, 9049, 60729, 450137, 3650561, 32152715, 305617486, 3117956778, 33982715596, 394052472343, 4843715202986, 62911628650900, 860907239890595, 12380145642957241] "" "Class ", 3798, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 5, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 5, 4], [0, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {}, {}], [[3, 4, 1, 2, 5], {2, 3, 4}, {}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {2, 3, 4}, {}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {}], [[4, 5, 1, 3, 2], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 280, 1447, 8430, 54636, 389652, 3030735, 25522572, 231293970, 2243930126, 23200643353, 254636367654, 2956354645724, 36196221062828, 466055395985863, 6295017790480012] "" "Class ", 3799, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 1, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 5, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 5, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 5, 3, 1, 2], [1, 1, 0, 0]]} "Class ", 3800, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {}, {}], [[2, 3, 1, 4, 5], {1, 2, 3}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2, 3}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {3}, {}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 1, 5], {3}, {}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 2, 4], {3}, {}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {3}, {}], [[3, 5, 2, 4, 1], {2, 3}, {}], [[4, 5, 1, 2, 3], {3}, {}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {3}, {}], [[4, 5, 2, 3, 1], {3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 282, 1482, 8844, 59002, 434934, 3509662, 30762926, 291001118, 2954364660, 32037453500, 369541824884, 4517371791690, 58332419283714, 793364398162596, 11335451638796264] "" "Class ", 3801, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {3}, {[0, 1, 0, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2, 3}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {3}, {}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 2, 4], {3}, {}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {2, 3}, {}], [[4, 5, 1, 2, 3], {3}, {}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 281, 1458, 8480, 54417, 381108, 2888423, 23531604, 204957020, 1899781892, 18666557561, 193758065169, 2118279259392, 24326119670484, 292744402632862, 3683768538745572] "" "Class ", 3802, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 1, 0]]} "Class ", 3803, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 1, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 5, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 5, 3, 1, 2], [1, 1, 1, 0]]} "Class ", 3804, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 5, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 5, 4], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 5, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 5, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 285, 1528, 9356, 64394, 492312, 4138729, 37942719, 376741788, 4027603073, 46123841061, 563324122644, 7308928811650, 100395239733357, 1455460307276960, 22208333433963518] "" "Class ", 3805, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 1, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 5, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 5, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 5, 3, 1, 2], [1, 0, 0, 1]]} "Class ", 3806, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 5, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 5, 4], [1, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2, 5], {2, 3, 4}, {}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {2, 3, 4}, {}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {}], [[4, 5, 1, 3, 2], {3}, {[0, 0, 1, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 280, 1447, 8430, 54636, 389652, 3030735, 25522572, 231293970, 2243930126, 23200643353, 254636367654, 2956354645724, 36196221062828, 466055395985863, 6295017790480012] "" "Class ", 3807, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 1, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 5, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 5, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 5, 3, 1, 2], [1, 1, 0, 1]]} "Class ", 3808, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 5, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 5, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]} "Class ", 3809, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 5, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 5, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 1]]} "Class ", 3810, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 5, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 5, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]} "Class ", 3811, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 1, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 5, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 5, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 3, 1, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 5, 3, 1, 2], [1, 1, 1, 1]]} "Class ", 3812, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1520, 9312, 64150, 491048, 4135572, 37994992, 378149546, 4053129096, 46545973448, 570165309888, 7420759698110, 102263323350056, 1487553034628444, 22777253171895824] "" "Class ", 3813, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 280, 1454, 8572, 56526, 411938, 3287926, 28527948, 267353370, 2691353586, 28963407190, 331824108784, 4032224067374, 51800785335414, 701471192465414, 9986640857094508] "" "Class ", 3814, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 4, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]} "Class ", 3815, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 1, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 5, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 4, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 4, 3, 1, 2], [1, 1, 0, 0]]} "Class ", 3816, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {}, {}], [[2, 3, 1, 4, 5], {1, 2, 3}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2, 3}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {3}, {}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 1, 5], {3}, {}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 2, 4], {3}, {}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {3}, {}], [[3, 5, 2, 4, 1], {2, 3}, {}], [[4, 5, 1, 2, 3], {3}, {}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {3}, {}], [[4, 5, 2, 3, 1], {3}, {}], [[4, 5, 3, 1, 2], {3}, {}], [[4, 5, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 283, 1502, 9095, 61779, 465104, 3843645, 34584944, 336536182, 3521093149, 39415173822, 470009032883, 5947734327647, 79603771515806, 1123426297203315, 16672873390988778] "" "Class ", 3817, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {3}, {[1, 0, 0, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2, 3}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {3}, {}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 2, 4], {3}, {}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {2, 3}, {}], [[4, 5, 1, 2, 3], {3}, {}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3, 4}, {[1, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 279, 1433, 8290, 53236, 374826, 2867588, 23669377, 209514311, 1978630868, 19848774407, 210701317002, 2358947703644, 27772102078402, 342925990073076, 4430707576570432] "" "Class ", 3818, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 1, 0]]} "Class ", 3819, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 5, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]} "Class ", 3820, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {}], [[4, 3, 2, 1], {1}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1520, 9312, 64150, 491048, 4135572, 37994992, 378149546, 4053129096, 46545973448, 570165309888, 7420759698110, 102263323350056, 1487553034628444, 22777253171895824] "" "Class ", 3821, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2, 3}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {2}, {}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 280, 1454, 8572, 56526, 411938, 3287926, 28527948, 267353370, 2691353586, 28963407190, 331824108784, 4032224067374, 51800785335414, 701471192465414, 9986640857094508] "" "Class ", 3822, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]} "Class ", 3823, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 5, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]} "Class ", 3824, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 4, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]} "Class ", 3825, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 4, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]} "Class ", 3826, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 4, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 1, 1]]} "Class ", 3827, " is:" {{[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 5, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[2, 1, 3, 4, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[4, 5, 3, 2, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]} "Class ", 3828, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}], [[4, 1, 2, 3, 5], {1, 2, 3}, {}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3}, {}], [[5, 2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 286, 1532, 9371, 64460, 492553, 4139892, 37957533, 377018462, 4032854333, 46219542639, 565024512076, 7339020025926, 100932815225597, 1465236571411864, 22390280022336292] "" "Class ", 3829, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1502, 9013, 60472, 448548, 3645006, 32204245, 307391995, 3152444406, 34570230469, 403682870074, 5000961538131, 65510825074506, 904773347005020, 13139599702457425] "" "Class ", 3830, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 4, 5, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 2, 1, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 4, 3, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 3, 4, 5, 1], [0, 1, 0, 0]]} "Class ", 3831, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 4, 5, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 2, 1, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 4, 3, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 3, 4, 5, 1], [1, 1, 0, 0]]} "Class ", 3832, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 4, 5, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 2, 1, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 4, 3, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 3, 4, 5, 1], [0, 0, 1, 0]]} "Class ", 3833, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 4, 5, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 2, 1, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 4, 3, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 3, 4, 5, 1], [1, 0, 1, 0]]} "Class ", 3834, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 4, 5, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 2, 1, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 4, 3, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 3, 4, 5, 1], [0, 1, 1, 0]]} "Class ", 3835, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 4, 5, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 2, 1, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 4, 3, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 3, 4, 5, 1], [1, 1, 1, 0]]} "Class ", 3836, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}], [[4, 1, 2, 3, 5], {1, 2, 3}, {}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {2, 3, 4}, {}], [[5, 2, 3, 4, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 283, 1491, 8902, 59388, 437778, 3532731, 30971411, 293106006, 2977954466, 32328532768, 373449593605, 4573737046962, 59196551217927, 807325416966122, 11571638805455704] "" "Class ", 3837, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 281, 1454, 8430, 53964, 377186, 2852895, 23181710, 201162476, 1854862462, 18096147848, 186109871200, 2011240744847, 22773998356904, 269526819758609, 3326402252712412] "" "Class ", 3838, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 4, 5, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 2, 1, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 3, 4, 5, 1], [0, 1, 0, 1]]} "Class ", 3839, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 4, 5, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 2, 1, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 4, 3, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 3, 4, 5, 1], [1, 1, 0, 1]]} "Class ", 3840, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 4, 5, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 4, 3, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 3, 4, 5, 1], [0, 0, 1, 1]]} "Class ", 3841, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 4, 5, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 2, 1, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 3, 4, 5, 1], [1, 0, 1, 1]]} "Class ", 3842, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 4, 5, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 2, 1, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 4, 3, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 3, 4, 5, 1], [0, 1, 1, 1]]} "Class ", 3843, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 4, 5, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 3, 4, 5, 1], [1, 1, 1, 1]]} "Class ", 3844, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 2, 4, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 4, 5, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 2, 1, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 4, 2, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 2, 4, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 1, 2, 4, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 4, 5, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 2, 1, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 4, 2, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 1, 2, 4, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 292, 1564, 9498, 64482, 483893, 3976341, 35511592, 342461741, 3546723011, 39260051902, 462565064786, 5779617080388, 76332907748958, 1062535114028762, 15547220204883899] "" "Class ", 3845, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 2, 4, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 4, 5, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 2, 1, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 4, 2, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 2, 4, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 2, 4, 5, 1], [0, 1, 0, 0]]} "Class ", 3846, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 2, 4, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 4, 5, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 2, 1, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 4, 2, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 2, 4, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 2, 4, 5, 1], [1, 1, 0, 0]]} "Class ", 3847, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 2, 4, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 4, 5, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 2, 1, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 4, 2, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 2, 4, 3], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 2, 4, 5, 1], [1, 0, 1, 0]]} "Class ", 3848, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 2, 4, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 4, 5, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 2, 1, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 4, 2, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 2, 4, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 2, 4, 5, 1], [0, 1, 1, 0]]} "Class ", 3849, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 2, 4, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 4, 5, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 2, 1, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 4, 2, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 2, 4, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 2, 4, 5, 1], [1, 1, 1, 0]]} "Class ", 3850, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 4, 5, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 2, 1, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 4, 5, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 2, 1, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 292, 1547, 9168, 59867, 426025, 3275270, 27014396, 237667343, 2219504621, 21910467550, 227823509399, 2487354415227, 28436221910030, 339576734804321, 4226534890618736] "" "Class ", 3851, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 4, 5, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 2, 1, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 2, 4, 5, 1], [0, 1, 0, 1]]} "Class ", 3852, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 4, 5, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 2, 1, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 4, 2, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 2, 4, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 2, 4, 5, 1], [1, 1, 0, 1]]} "Class ", 3853, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 2, 4, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 4, 5, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 2, 1, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 4, 2, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 2, 4, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 2, 4, 5, 1], [1, 0, 1, 1]]} "Class ", 3854, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 2, 4, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 4, 5, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 2, 1, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 4, 2, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 2, 4, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 2, 4, 5, 1], [0, 1, 1, 1]]} "Class ", 3855, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 2, 4, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 4, 5, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 2, 1, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 4, 2, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 2, 4, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 2, 4, 5, 1], [1, 1, 1, 1]]} "Class ", 3856, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 3, 2, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 3, 5, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 3, 1, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 3, 4, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 3, 2, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 4, 3, 5, 1], [0, 1, 0, 0]]} "Class ", 3857, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 3, 2, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 3, 5, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 3, 1, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 3, 4, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 3, 2, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 4, 3, 5, 1], [1, 1, 0, 0]]} "Class ", 3858, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 3, 2, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 3, 5, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 3, 1, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 3, 4, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 3, 2, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 4, 3, 5, 1], [0, 0, 1, 0]]} "Class ", 3859, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 3, 2, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 3, 1, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 3, 4, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 3, 2, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 1, 0]]} "Class ", 3860, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 3, 2, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 3, 5, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 3, 1, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 3, 4, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 3, 2, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 4, 3, 5, 1], [0, 1, 1, 0]]} "Class ", 3861, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 3, 2, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 3, 5, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 3, 1, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 3, 4, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 3, 2, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 4, 3, 5, 1], [1, 1, 1, 0]]} "Class ", 3862, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 3, 5, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 3, 1, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 4, 3, 5, 1], [0, 1, 0, 1]]} "Class ", 3863, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 3, 5, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 3, 1, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 3, 4, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 3, 2, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 4, 3, 5, 1], [1, 1, 0, 1]]} "Class ", 3864, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 3, 2, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 3, 5, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 3, 1, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 3, 4, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 3, 2, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 4, 3, 5, 1], [0, 0, 1, 1]]} "Class ", 3865, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 3, 2, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 3, 1, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 3, 4, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 3, 2, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 4, 3, 5, 1], [1, 0, 1, 1]]} "Class ", 3866, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 3, 2, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 3, 5, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 3, 1, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 3, 4, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 3, 2, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 4, 3, 5, 1], [0, 1, 1, 1]]} "Class ", 3867, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 3, 2, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 3, 5, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 3, 1, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 3, 4, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 3, 2, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 4, 3, 5, 1], [1, 1, 1, 1]]} "Class ", 3868, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 3, 5, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 3, 1, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 3, 2, 4], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 3, 5, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 3, 1, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 3, 2, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 285, 1526, 9340, 64307, 491960, 4140064, 38007508, 377997872, 4048489755, 46457936771, 568663629576, 7395711464794, 101842275031299, 1480325871459164, 22649726295680881] "" "Class ", 3869, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 3, 5, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 3, 1, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 3, 2, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 3, 5, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 3, 1, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 3, 2, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 282, 1481, 8831, 58941, 435298, 3524296, 31040340, 295470815, 3022813065, 33076071128, 385463953621, 4766501373132, 62333517198444, 859531712852072, 12464141291678573] "" "Class ", 3870, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 3, 5, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 3, 1, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 3, 2, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 2, 3, 5, 1], [0, 1, 0, 0]]} "Class ", 3871, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 3, 5, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 3, 1, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 3, 2, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 2, 3, 5, 1], [1, 1, 0, 0]]} "Class ", 3872, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 3, 5, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 3, 1, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 3, 2, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 2, 3, 5, 1], [0, 0, 1, 0]]} "Class ", 3873, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 3, 5, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 3, 1, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 3, 2, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 2, 3, 5, 1], [1, 0, 1, 0]]} "Class ", 3874, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 3, 5, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 3, 1, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 3, 2, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 2, 3, 5, 1], [0, 1, 1, 0]]} "Class ", 3875, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 3, 5, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 3, 1, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 3, 2, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 2, 3, 5, 1], [1, 1, 1, 0]]} "Class ", 3876, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 3, 5, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 3, 1, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 3, 5, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 3, 1, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}], [[4, 1, 2, 3, 5], {1, 2, 3}, {}], [[5, 1, 2, 3, 4], {2}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 281, 1463, 8611, 56517, 409136, 3237315, 27786126, 257055989, 2549392532, 26979577095, 303434132326, 3613913062797, 45436182933905, 601324492243455, 8355913898627929] "" "Class ", 3877, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 3, 5, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 3, 1, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 3, 5, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 3, 1, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {[0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 278, 1407, 7899, 48562, 323778, 2322902, 17817819, 145339035, 1254976436, 11426798080, 109343443518, 1096409950290, 11490844444344, 125586307459054, 1428435609561185] "" "Class ", 3878, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 3, 5, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 3, 1, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 2, 3, 5, 1], [0, 1, 0, 1]]} "Class ", 3879, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 3, 5, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 3, 1, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 3, 2, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 2, 3, 5, 1], [1, 1, 0, 1]]} "Class ", 3880, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 3, 5, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 3, 1, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 3, 2, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 2, 3, 5, 1], [0, 0, 1, 1]]} "Class ", 3881, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 3, 5, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 3, 1, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 3, 2, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 2, 3, 5, 1], [1, 0, 1, 1]]} "Class ", 3882, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 3, 5, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 3, 1, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 3, 2, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 2, 3, 5, 1], [0, 1, 1, 1]]} "Class ", 3883, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 3, 5, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 3, 1, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 3, 2, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 3, 4, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 2, 3, 5, 1], [1, 1, 1, 1]]} "Class ", 3884, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 4, 2, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 2, 5, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 4, 1, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 2, 4, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 4, 2, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 4, 2, 5, 1], [0, 1, 0, 0]]} "Class ", 3885, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 4, 2, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 2, 5, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 4, 1, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 2, 4, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 4, 2, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 4, 2, 5, 1], [1, 1, 0, 0]]} "Class ", 3886, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 4, 2, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 4, 1, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 2, 4, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 4, 2, 3], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 1, 0]]} "Class ", 3887, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 4, 2, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 4, 1, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 2, 4, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 4, 2, 3], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 0]]} "Class ", 3888, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 4, 2, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 2, 5, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 4, 1, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 2, 4, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 4, 2, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 4, 2, 5, 1], [0, 1, 1, 0]]} "Class ", 3889, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 4, 2, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 4, 1, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 2, 4, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 4, 2, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 0]]} "Class ", 3890, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 2, 5, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 4, 1, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 4, 2, 5, 1], [0, 1, 0, 1]]} "Class ", 3891, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 2, 5, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 4, 1, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 2, 4, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 4, 2, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 4, 2, 5, 1], [1, 1, 0, 1]]} "Class ", 3892, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 4, 2, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 4, 1, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 2, 4, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 4, 2, 3], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[3, 4, 2, 5, 1], [0, 0, 1, 1]]} "Class ", 3893, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 4, 2, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 4, 1, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 2, 4, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 4, 2, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 1]]} "Class ", 3894, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 4, 2, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 2, 5, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 4, 1, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 2, 4, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 4, 2, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 4, 2, 5, 1], [0, 1, 1, 1]]} "Class ", 3895, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 4, 2, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 4, 1, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 2, 4, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 4, 2, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 1]]} "Class ", 3896, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 4, 3, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 2, 5, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 4, 1, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 2, 3, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 4, 3, 2], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 3, 2, 5, 1], [0, 1, 0, 0]]} "Class ", 3897, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 4, 3, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 2, 5, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 4, 1, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 2, 3, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 4, 3, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 3, 2, 5, 1], [1, 1, 0, 0]]} "Class ", 3898, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 4, 3, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 2, 5, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 4, 1, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 2, 3, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 4, 3, 2], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 3, 2, 5, 1], [0, 0, 1, 0]]} "Class ", 3899, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 4, 3, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 4, 1, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 2, 3, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 4, 3, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 1, 0]]} "Class ", 3900, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 4, 3, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 2, 5, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 4, 1, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 2, 3, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 4, 3, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 3, 2, 5, 1], [0, 1, 1, 0]]} "Class ", 3901, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 4, 3, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 2, 5, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 4, 1, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 2, 3, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 4, 3, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 3, 2, 5, 1], [1, 1, 1, 0]]} "Class ", 3902, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 2, 5, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 4, 1, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 3, 2, 5, 1], [0, 1, 0, 1]]} "Class ", 3903, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 2, 5, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 4, 1, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 2, 3, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 4, 3, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 3, 2, 5, 1], [1, 1, 0, 1]]} "Class ", 3904, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 4, 3, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 2, 5, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 4, 1, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 2, 3, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 4, 3, 2], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 3, 2, 5, 1], [0, 0, 1, 1]]} "Class ", 3905, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 4, 3, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 4, 1, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 2, 3, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 4, 3, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 3, 2, 5, 1], [1, 0, 1, 1]]} "Class ", 3906, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 4, 3, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 2, 5, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 4, 1, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 2, 3, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 4, 3, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 3, 2, 5, 1], [0, 1, 1, 1]]} "Class ", 3907, " is:" {{[[1, 3, 2], [0, 0]], [[5, 1, 4, 3, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 2, 5, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 4, 1, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 5, 2, 3, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 1, 4, 3, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 3, 2, 5, 1], [1, 1, 1, 1]]} "Class ", 3908, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 4, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 2, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 5, 3, 2], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 4, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 2, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 5, 3, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}], [[4, 2, 1, 3, 5], {1, 2, 3}, {}], [[5, 2, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 287, 1545, 9510, 65873, 506952, 4291619, 39632728, 396495617, 4271773813, 49310859987, 607163554942, 7943249075075, 110030811585336, 1608834761769158, 24761956400680358] "" "Class ", 3909, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 4, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 2, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 5, 3, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 4, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 2, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 5, 3, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 286, 1530, 9336, 63973, 486250, 4060735, 36955200, 364029218, 3859026808, 43804248145, 530096812934, 6812761197530, 92669576675744, 1330070928110835, 20088505228834896] "" "Class ", 3910, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 4, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 2, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 5, 3, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 3, 5, 4, 1], [0, 1, 0, 0]]} "Class ", 3911, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 4, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 2, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 5, 3, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 3, 5, 4, 1], [1, 1, 0, 0]]} "Class ", 3912, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 4, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 2, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 5, 3, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 3, 5, 4, 1], [0, 0, 1, 0]]} "Class ", 3913, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 4, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 2, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 5, 3, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 3, 5, 4, 1], [1, 0, 1, 0]]} "Class ", 3914, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 4, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 2, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 5, 3, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 3, 5, 4, 1], [0, 1, 1, 0]]} "Class ", 3915, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 4, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 2, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 5, 3, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 3, 5, 4, 1], [1, 1, 1, 0]]} "Class ", 3916, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 4, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 2, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 4, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 2, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {}], [[4, 2, 1, 3, 5], {1, 2, 3}, {}], [[5, 2, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1505, 9061, 61081, 455647, 3725704, 33132067, 318353029, 3286771347, 36285914338, 426566135858, 5319878625938, 70153796781397, 975333914816392, 14257898543940150] "" "Class ", 3917, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 4, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 2, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 4, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 2, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 283, 1488, 8852, 58710, 429157, 3426132, 29651480, 276483211, 2763142252, 29463748354, 333894870905, 4007344266444, 50778868436259, 677459506350089, 9492285604140301] "" "Class ", 3918, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 4, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 2, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 3, 5, 4, 1], [0, 1, 0, 1]]} "Class ", 3919, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 4, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 2, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 5, 3, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 3, 5, 4, 1], [1, 1, 0, 1]]} "Class ", 3920, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 4, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 2, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 5, 3, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 3, 5, 4, 1], [0, 0, 1, 1]]} "Class ", 3921, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 4, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 2, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 5, 3, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 3, 5, 4, 1], [1, 0, 1, 1]]} "Class ", 3922, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 4, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 2, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 5, 3, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 3, 5, 4, 1], [0, 1, 1, 1]]} "Class ", 3923, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 5, 4, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 3, 1, 2, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 5, 3, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 1, 3, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 3, 5, 4, 1], [1, 1, 1, 1]]} "Class ", 3924, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 1, 4, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 5, 4, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 1, 2, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 5, 2, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 1, 4, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 2, 1, 4, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 5, 4, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 1, 2, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 5, 2, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 2, 1, 4, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {[0, 0, 1, 0, 0]}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 293, 1581, 9718, 67015, 512509, 4303785, 39367646, 389636589, 4148625962, 47284797151, 574418635548, 7409103141143, 101125932569120, 1456146328982806, 22060355535441350] "" "Class ", 3925, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 1, 4, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 5, 4, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 1, 2, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 5, 2, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 1, 4, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 2, 5, 4, 1], [0, 1, 0, 0]]} "Class ", 3926, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 1, 4, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 5, 4, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 1, 2, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 5, 2, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 1, 4, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 2, 5, 4, 1], [1, 1, 0, 0]]} "Class ", 3927, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 1, 4, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 5, 4, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 1, 2, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 5, 2, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 1, 4, 3], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 2, 5, 4, 1], [1, 0, 1, 0]]} "Class ", 3928, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 1, 4, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 5, 4, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 1, 2, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 5, 2, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 1, 4, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 2, 5, 4, 1], [0, 1, 1, 0]]} "Class ", 3929, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 1, 4, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 5, 4, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 1, 2, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 5, 2, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 1, 4, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 2, 5, 4, 1], [1, 1, 1, 0]]} "Class ", 3930, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 5, 4, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 1, 2, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 5, 4, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 1, 2, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 293, 1572, 9548, 64679, 483124, 3942274, 34875300, 332376153, 3394302995, 36972481597, 427832463302, 5240894516789, 67751197531978, 921714732540458, 13162980528712885] "" "Class ", 3931, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 5, 4, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 1, 2, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 2, 5, 4, 1], [0, 1, 0, 1]]} "Class ", 3932, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 5, 4, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 1, 2, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 5, 2, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 1, 4, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 2, 5, 4, 1], [1, 1, 0, 1]]} "Class ", 3933, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 1, 4, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 5, 4, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 1, 2, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 5, 2, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 1, 4, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 2, 5, 4, 1], [1, 0, 1, 1]]} "Class ", 3934, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 1, 4, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 5, 4, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 1, 2, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 5, 2, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 1, 4, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 2, 5, 4, 1], [0, 1, 1, 1]]} "Class ", 3935, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 1, 4, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 5, 4, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 4, 1, 2, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 5, 2, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 1, 4, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 2, 5, 4, 1], [1, 1, 1, 1]]} "Class ", 3936, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 3, 4, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 3, 2, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 5, 2], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 3, 4, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 3, 2, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 5, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {}], [[4, 2, 3, 1, 5], {1, 2, 3}, {}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2}, {}], [[5, 3, 4, 1, 2], {1, 2}, {}], [[5, 3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 289, 1568, 9729, 67926, 526977, 4496972, 41864521, 422210072, 4585575943, 53360893605, 662340286623, 8735102972699, 121977184425579, 1797919689292006, 27895769117973847] "" "Class ", 3937, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 3, 2, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 5, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 3, 2, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 5, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 286, 1532, 9341, 63875, 484182, 4028955, 36513338, 358018732, 3776287183, 42635988148, 513055488769, 6555028528691, 88621231916080, 1263985650398020, 18967441171684385] "" "Class ", 3938, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 3, 4, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 3, 2, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 5, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 3, 4, 1], [0, 1, 0, 0]]} "Class ", 3939, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 3, 4, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 3, 2, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 5, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 3, 4, 1], [1, 1, 0, 0]]} "Class ", 3940, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 3, 4, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 3, 2, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 5, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 3, 4, 1], [0, 0, 1, 0]]} "Class ", 3941, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 3, 2, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 5, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 1, 0]]} "Class ", 3942, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 3, 4, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 3, 2, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 5, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 3, 4, 1], [0, 1, 1, 0]]} "Class ", 3943, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 3, 4, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 3, 2, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 5, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 3, 4, 1], [1, 1, 1, 0]]} "Class ", 3944, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 3, 4, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 3, 2, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 3, 4, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 3, 2, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {}], [[4, 2, 3, 1, 5], {1, 2, 3}, {}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {2, 3}, {}], [[5, 3, 4, 1, 2], {2, 3}, {}], [[5, 3, 4, 2, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 285, 1522, 9260, 63186, 477839, 3966819, 35863278, 350756373, 3690069132, 41552003799, 498659586677, 6353621512567, 85660170208356, 1218338715363383, 18231068419834333] "" "Class ", 3945, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 3, 2, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 3, 2, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 282, 1473, 8654, 56264, 399950, 3079611, 25494716, 225518995, 2120491416, 21100234542, 221349577730, 2439877207353, 28176473477998, 340024680915781, 4277952067939418] "" "Class ", 3946, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 3, 4, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 3, 2, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 3, 4, 1], [0, 1, 0, 1]]} "Class ", 3947, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 3, 4, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 3, 2, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 5, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 3, 4, 1], [1, 1, 0, 1]]} "Class ", 3948, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 3, 4, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 3, 2, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 5, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 3, 4, 1], [0, 0, 1, 1]]} "Class ", 3949, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 3, 2, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 5, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 3, 4, 1], [1, 0, 1, 1]]} "Class ", 3950, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 3, 4, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 3, 2, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 5, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 3, 4, 1], [0, 1, 1, 1]]} "Class ", 3951, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 3, 4, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 3, 2, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 5, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 3, 1, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 3, 4, 1], [1, 1, 1, 1]]} "Class ", 3952, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 3, 4, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 3, 2, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 2, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 3, 4, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 3, 2, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 2, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}], [[4, 1, 2, 3, 5], {1, 2, 3}, {}], [[5, 1, 2, 3, 4], {1, 2, 3}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3}, {}], [[5, 2, 3, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 286, 1545, 9554, 66456, 513468, 4364140, 40467204, 406506388, 4397545378, 50970099826, 630159448790, 8277797356842, 115133716613902, 1690329083960506, 26122600983724198] "" "Class ", 3953, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 2, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 2, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2}, {[1, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 283, 1497, 9008, 60729, 453173, 3707070, 32983728, 317112046, 3275905001, 36186375110, 425609053575, 5310150337341, 70047770850077, 974066673733426, 14240834903789419] "" "Class ", 3954, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 3, 4, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 3, 2, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 2, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 2, 3, 4, 1], [0, 1, 0, 0]]} "Class ", 3955, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 3, 4, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 3, 2, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 2, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 2, 3, 4, 1], [1, 1, 0, 0]]} "Class ", 3956, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 3, 4, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 3, 2, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 2, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 2, 3, 4, 1], [0, 0, 1, 0]]} "Class ", 3957, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 2, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 1, 0]]} "Class ", 3958, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 3, 4, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 3, 2, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 2, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 2, 3, 4, 1], [0, 1, 1, 0]]} "Class ", 3959, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 3, 4, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 3, 2, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 2, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 2, 3, 4, 1], [1, 1, 1, 0]]} "Class ", 3960, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 3, 4, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 3, 2, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 3, 4, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 3, 2, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}], [[4, 1, 2, 3, 5], {1, 2, 3}, {}], [[5, 1, 2, 3, 4], {2}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {2, 3, 4}, {}], [[5, 2, 3, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 282, 1483, 8870, 59439, 440708, 3580055, 31616592, 301591668, 3090314074, 33851270035, 394734727760, 4881823944570, 63822855627502, 879451336453937, 12739192446538186] "" "Class ", 3961, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {[1, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 280, 1443, 8335, 53202, 371110, 2803687, 22775577, 197756766, 1826155109, 17857823392, 184243664924, 1999031068151, 22743861908361, 270656718418149, 3361177278603114] "" "Class ", 3962, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 3, 4, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 3, 2, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 2, 3, 4, 1], [0, 1, 0, 1]]} "Class ", 3963, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 3, 4, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 3, 2, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 2, 3, 4, 1], [1, 1, 0, 1]]} "Class ", 3964, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 3, 4, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 3, 2, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 2, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 2, 3, 4, 1], [0, 0, 1, 1]]} "Class ", 3965, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 3, 2, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 2, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 2, 3, 4, 1], [1, 0, 1, 1]]} "Class ", 3966, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 3, 4, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 3, 2, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 2, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 2, 3, 4, 1], [0, 1, 1, 1]]} "Class ", 3967, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 3, 4, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 3, 2, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 3, 2, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 3, 4, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 2, 3, 4, 1], [1, 1, 1, 1]]} "Class ", 3968, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 4, 2, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 2, 5, 3], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 4, 2, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 2, 5, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {}], [[4, 2, 3, 1, 5], {1, 2, 3}, {}], [[5, 2, 3, 1, 4], {1, 2, 3}, {}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {1, 2}, {}], [[5, 3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 288, 1561, 9667, 67368, 521746, 4444690, 41304586, 415833687, 4508430418, 52371273728, 648918322231, 8543113824687, 119087408036184, 1752251986347725, 27139615958284014] "" "Class ", 3969, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 4, 2, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 2, 5, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 4, 2, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 2, 5, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 286, 1534, 9363, 64097, 486470, 4053083, 36776079, 361011636, 3812090289, 43085769825, 518989629557, 6637210507828, 89814469837974, 1282124245675854, 19255709923824470] "" "Class ", 3970, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 2, 4, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 4, 2, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 2, 5, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 5, 2, 4, 1], [0, 1, 0, 0]]} "Class ", 3971, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 2, 4, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 4, 2, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 2, 5, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 5, 2, 4, 1], [1, 1, 0, 0]]} "Class ", 3972, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 4, 2, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 2, 5, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 1, 0]]} "Class ", 3973, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 4, 2, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 2, 5, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 1, 0]]} "Class ", 3974, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 2, 4, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 4, 2, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 2, 5, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 5, 2, 4, 1], [0, 1, 1, 0]]} "Class ", 3975, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 2, 4, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 4, 2, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 2, 5, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 5, 2, 4, 1], [1, 1, 1, 0]]} "Class ", 3976, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 4, 2, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 4, 2, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {}], [[4, 2, 3, 1, 5], {1, 2, 3}, {}], [[5, 2, 3, 1, 4], {2, 3}, {}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {2, 3}, {}], [[5, 3, 4, 2, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1509, 9128, 61895, 464848, 3830016, 34348064, 333067355, 3472405591, 38732237645, 460258410406, 5804723422832, 77438987096094, 1089528367925384, 16123217003850250] "" "Class ", 3977, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 4, 2, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 4, 2, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 282, 1473, 8654, 56264, 399950, 3079611, 25494716, 225518995, 2120491416, 21100234542, 221349577730, 2439877207353, 28176473477998, 340024680915781, 4277952067939418] "" "Class ", 3978, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 2, 4, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 4, 2, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 5, 2, 4, 1], [0, 1, 0, 1]]} "Class ", 3979, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 2, 4, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 4, 2, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 2, 5, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 5, 2, 4, 1], [1, 1, 0, 1]]} "Class ", 3980, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 4, 2, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 2, 5, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[3, 5, 2, 4, 1], [0, 0, 1, 1]]} "Class ", 3981, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 4, 2, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 2, 5, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 5, 2, 4, 1], [1, 0, 1, 1]]} "Class ", 3982, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 2, 4, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 4, 2, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 2, 5, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 5, 2, 4, 1], [0, 1, 1, 1]]} "Class ", 3983, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 2, 4, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 4, 2, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 2, 5, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 4, 1, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 5, 2, 4, 1], [1, 1, 1, 1]]} "Class ", 3984, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 4, 3, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 2, 4, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 4, 2, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 2, 3, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 4, 3, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 3, 2, 4, 1], [0, 1, 0, 0]]} "Class ", 3985, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 4, 3, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 2, 4, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 4, 2, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 2, 3, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 4, 3, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 3, 2, 4, 1], [1, 1, 0, 0]]} "Class ", 3986, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 4, 3, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 2, 4, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 4, 2, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 2, 3, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 4, 3, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 3, 2, 4, 1], [0, 0, 1, 0]]} "Class ", 3987, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 4, 3, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 2, 3, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 4, 3, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 1, 0]]} "Class ", 3988, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 4, 3, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 2, 4, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 4, 2, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 2, 3, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 4, 3, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 3, 2, 4, 1], [0, 1, 1, 0]]} "Class ", 3989, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 4, 3, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 2, 4, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 4, 2, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 2, 3, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 4, 3, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 3, 2, 4, 1], [1, 1, 1, 0]]} "Class ", 3990, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 2, 4, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 4, 2, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 2, 3, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 3, 2, 4, 1], [0, 1, 0, 1]]} "Class ", 3991, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 2, 4, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 4, 2, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 2, 3, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 3, 2, 4, 1], [1, 1, 0, 1]]} "Class ", 3992, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 4, 3, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 2, 4, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 4, 2, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 2, 3, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 4, 3, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 3, 2, 4, 1], [0, 0, 1, 1]]} "Class ", 3993, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 4, 3, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 2, 3, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 4, 3, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 1, 1]]} "Class ", 3994, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 4, 3, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 2, 4, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 4, 2, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 2, 3, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 4, 3, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 3, 2, 4, 1], [0, 1, 1, 1]]} "Class ", 3995, " is:" {{[[1, 3, 2], [0, 0]], [[5, 2, 4, 3, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 2, 4, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 4, 2, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 4, 2, 3, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 2, 4, 3, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 3, 2, 4, 1], [1, 1, 1, 1]]} "Class ", 3996, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 5, 4, 2], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 5, 4, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {1}, {}], [[4, 3, 1, 2, 5], {1, 2, 3}, {}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3}, {}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 289, 1568, 9735, 68029, 528198, 4511037, 42028713, 424197822, 4610777446, 53696332276, 667027756372, 8803839642101, 123033694549056, 1814918287073573, 28181652222102648] "" "Class ", 3997, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 5, 4, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 5, 4, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 287, 1544, 9484, 65466, 501572, 4223703, 38776841, 385471672, 4124970565, 47278759211, 577850323528, 7502173191626, 103107499788118, 1495525807792333, 22829844036097789] "" "Class ", 3998, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 3, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 3, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 5, 4, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 4, 5, 3, 1], [0, 1, 0, 0]]} "Class ", 3999, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 3, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 3, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 5, 4, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 4, 5, 3, 1], [1, 1, 0, 0]]} "Class ", 4000, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 3, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 3, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 5, 4, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 4, 5, 3, 1], [0, 0, 1, 0]]} "Class ", 4001, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 3, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 5, 4, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 1, 0]]} "Class ", 4002, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 3, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 3, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 5, 4, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 4, 5, 3, 1], [0, 1, 1, 0]]} "Class ", 4003, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 3, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 3, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 5, 4, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 4, 5, 3, 1], [1, 1, 1, 0]]} "Class ", 4004, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {2}, {}], [[4, 3, 1, 2, 5], {1, 2, 3}, {}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {2, 3}, {}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 286, 1531, 9338, 63878, 484175, 4027115, 36466539, 357125143, 3761032309, 42385791809, 508973347494, 6487659525144, 87486488910977, 1244373957000935, 18618584806113869] "" "Class ", 4005, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {1}, {[0, 0, 0, 1, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1502, 8993, 59995, 440536, 3526631, 30543560, 284381319, 2831211640, 30000944202, 337021222621, 3999671386007, 49991798473392, 656282369069683, 9026809352274482] "" "Class ", 4006, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 3, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 3, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 4, 5, 3, 1], [0, 1, 0, 1]]} "Class ", 4007, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 3, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 3, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 5, 4, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 4, 5, 3, 1], [1, 1, 0, 1]]} "Class ", 4008, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 3, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 3, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 5, 4, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 4, 5, 3, 1], [0, 0, 1, 1]]} "Class ", 4009, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 3, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 5, 4, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 4, 5, 3, 1], [1, 0, 1, 1]]} "Class ", 4010, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 3, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 3, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 5, 4, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 4, 5, 3, 1], [0, 1, 1, 1]]} "Class ", 4011, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 4, 5, 3, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 2, 1, 3, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 5, 4, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 1, 2, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 4, 5, 3, 1], [1, 1, 1, 1]]} "Class ", 4012, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 1, 4, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 5, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 1, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 5, 2, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 1, 4, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 3, 1, 4, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 5, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 1, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 5, 2, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 3, 1, 4, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 293, 1584, 9770, 67647, 519609, 4383170, 40274656, 400390938, 4281808588, 49011587133, 597879554943, 7743014228093, 106100278944753, 1533626616933105, 23320600165792991] "" "Class ", 4013, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 1, 4, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 5, 3, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 1, 3, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 5, 2, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 1, 4, 2], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 2, 5, 3, 1], [0, 1, 0, 0]]} "Class ", 4014, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 1, 4, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 5, 3, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 1, 3, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 5, 2, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 1, 4, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 2, 5, 3, 1], [1, 1, 0, 0]]} "Class ", 4015, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 1, 4, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 5, 3, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 1, 3, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 5, 2, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 1, 4, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 2, 5, 3, 1], [1, 0, 1, 0]]} "Class ", 4016, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 1, 4, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 5, 3, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 1, 3, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 5, 2, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 1, 4, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 2, 5, 3, 1], [0, 1, 1, 0]]} "Class ", 4017, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 1, 4, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 5, 3, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 1, 3, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 5, 2, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 1, 4, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 2, 5, 3, 1], [1, 1, 1, 0]]} "Class ", 4018, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 5, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 1, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 5, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 1, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {[0, 1, 0, 0, 0]}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 293, 1575, 9599, 65277, 489524, 4010183, 35609369, 340580076, 3489805891, 38133610471, 442590811817, 5437000954477, 70473641907737, 961163597285711, 13758984013345294] "" "Class ", 4019, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 5, 3, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 1, 3, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 2, 5, 3, 1], [0, 1, 0, 1]]} "Class ", 4020, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 5, 3, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 1, 3, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 5, 2, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 1, 4, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 2, 5, 3, 1], [1, 1, 0, 1]]} "Class ", 4021, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 1, 4, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 5, 3, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 1, 3, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 5, 2, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 1, 4, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 2, 5, 3, 1], [1, 0, 1, 1]]} "Class ", 4022, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 1, 4, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 5, 3, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 1, 3, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 5, 2, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 1, 4, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 2, 5, 3, 1], [0, 1, 1, 1]]} "Class ", 4023, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 1, 4, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 2, 5, 3, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 4, 1, 3, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 5, 2, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 1, 4, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 2, 5, 3, 1], [1, 1, 1, 1]]} "Class ", 4024, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {}, {}], [[4, 3, 2, 1, 5], {1, 2, 3}, {}], [[5, 3, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {1, 2, 3}, {}], [[5, 4, 3, 1, 2], {1, 2, 3}, {}], [[5, 4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 290, 1578, 9818, 68748, 534931, 4578333, 42747962, 432396863, 4710107947, 54972132138, 684357957147, 9052173352767, 126778629750385, 1874219257893868, 29165613708694180] "" "Class ", 4025, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 287, 1547, 9511, 65739, 504591, 4258079, 39184608, 390540747, 4190920655, 48177324436, 590673547952, 7693686505044, 106097727197821, 1544280907933365, 23658951557515861] "" "Class ", 4026, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 3, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 3, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 5, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 4, 3, 1], [0, 1, 0, 0]]} "Class ", 4027, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 3, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 3, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 5, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 4, 3, 1], [1, 1, 0, 0]]} "Class ", 4028, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 3, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 3, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 5, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 4, 3, 1], [0, 0, 1, 0]]} "Class ", 4029, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 5, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 1, 0]]} "Class ", 4030, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 3, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 3, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 5, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 4, 3, 1], [0, 1, 1, 0]]} "Class ", 4031, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 3, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 3, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 5, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 4, 3, 1], [1, 1, 1, 0]]} "Class ", 4032, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {}, {}], [[4, 3, 2, 1, 5], {1, 2, 3}, {}], [[5, 3, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {2, 3}, {}], [[5, 4, 3, 1, 2], {2, 3}, {}], [[5, 4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 288, 1558, 9622, 66798, 514837, 4361793, 40290535, 402996673, 4339277819, 50044549893, 615468573087, 8040471699464, 111196662008972, 1622949542930583, 24930197390042833] "" "Class ", 4033, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 286, 1531, 9315, 63470, 478342, 3948614, 35420318, 342980138, 3564906199, 39580994790, 467470620911, 5851202155913, 77363719169803, 1077366383536041, 15761080537929240] "" "Class ", 4034, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 3, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 3, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 4, 3, 1], [0, 1, 0, 1]]} "Class ", 4035, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 3, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 3, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 5, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 4, 3, 1], [1, 1, 0, 1]]} "Class ", 4036, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 3, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 3, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 5, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 4, 3, 1], [0, 0, 1, 1]]} "Class ", 4037, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 3, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 5, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 4, 3, 1], [1, 0, 1, 1]]} "Class ", 4038, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 3, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 3, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 5, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[2, 5, 4, 3, 1], [0, 1, 1, 1]]} "Class ", 4039, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 5, 4, 3, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[4, 1, 2, 3, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 5, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 2, 1, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[2, 5, 4, 3, 1], [1, 1, 1, 1]]} "Class ", 4040, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 2, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 2, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}], [[4, 2, 1, 3, 5], {1, 2, 3}, {}], [[5, 2, 1, 3, 4], {1, 2, 3}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 287, 1559, 9686, 67661, 525042, 4481882, 41739683, 421111910, 4575351240, 53261649096, 661354259392, 8725350710092, 121886363272325, 1797249462786001, 27895748585066474] "" "Class ", 4041, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 2, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 2, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {[1, 0, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 285, 1530, 9377, 64543, 492908, 4134972, 37799426, 373974491, 3981173609, 45375266032, 551271795146, 7111823055538, 97092462325660, 1398488120609433, 21194113092692806] "" "Class ", 4042, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 3, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 3, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 2, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 2, 4, 3, 1], [0, 1, 0, 0]]} "Class ", 4043, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 3, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 3, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 2, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 2, 4, 3, 1], [1, 1, 0, 0]]} "Class ", 4044, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 3, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 3, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 2, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 2, 4, 3, 1], [0, 0, 1, 0]]} "Class ", 4045, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 3, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 2, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 1, 0]]} "Class ", 4046, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 3, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 3, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 2, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 2, 4, 3, 1], [0, 1, 1, 0]]} "Class ", 4047, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 3, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 3, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 2, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 2, 4, 3, 1], [1, 1, 1, 0]]} "Class ", 4048, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {}], [[4, 2, 1, 3, 5], {1, 2, 3}, {}], [[5, 2, 1, 3, 4], {2, 3}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 285, 1532, 9412, 64912, 496433, 4170109, 38172519, 378189840, 4031628296, 46013435376, 559794596683, 7231781367805, 98867962816829, 1426065868038025, 21642733080933927] "" "Class ", 4049, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {[1, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 283, 1499, 9026, 60741, 451341, 3667666, 32342626, 307518605, 3135353238, 34116500567, 394567085941, 4832678254618, 62485370230830, 850463215290050, 12153716174173471] "" "Class ", 4050, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 3, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 3, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 2, 4, 3, 1], [0, 1, 0, 1]]} "Class ", 4051, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 3, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 3, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 2, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 2, 4, 3, 1], [1, 1, 0, 1]]} "Class ", 4052, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 3, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 3, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 2, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 2, 4, 3, 1], [0, 0, 1, 1]]} "Class ", 4053, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 3, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 2, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 2, 4, 3, 1], [1, 0, 1, 1]]} "Class ", 4054, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 3, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 3, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 2, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 2, 4, 3, 1], [0, 1, 1, 1]]} "Class ", 4055, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 2, 4, 3, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 4, 2, 3, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 4, 2, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 2, 4, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 2, 4, 3, 1], [1, 1, 1, 1]]} "Class ", 4056, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 4, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 5, 4], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 4, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 5, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {}], [[4, 2, 3, 1, 5], {1, 2, 3}, {}], [[5, 2, 3, 1, 4], {1, 2, 3}, {}], [[5, 2, 4, 1, 3], {1, 2}, {}], [[5, 3, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 288, 1565, 9718, 67899, 527151, 4501857, 41939961, 423275034, 4600484374, 53573260352, 665458864011, 8782604672971, 122729521862422, 1810322043274301, 28108587704221875] "" "Class ", 4057, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 4, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 5, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 4, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 5, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 287, 1546, 9483, 65273, 498155, 4173654, 38080100, 375837066, 3989532881, 45321727845, 548624483045, 7049786511125, 95839110148432, 1374254599637933, 20728803295456014] "" "Class ", 4058, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 5, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 5, 4], [0, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {}, {}], [[3, 4, 1, 2, 5], {2, 3, 4}, {}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {2, 3, 4}, {}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {}], [[4, 5, 1, 3, 2], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1511, 9160, 62274, 468822, 3869675, 34740630, 336977795, 3511501828, 39117990799, 463863884126, 5833104744033, 77527657808386, 1085851728724686, 15983912759556558] "" "Class ", 4059, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 2, 3, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 4, 3, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 5, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 5, 2, 3, 1], [1, 1, 0, 0]]} "Class ", 4060, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 4, 3, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 5, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 1, 0]]} "Class ", 4061, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 4, 3, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 5, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 1, 0]]} "Class ", 4062, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 5, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 1, 0]]} "Class ", 4063, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 2, 3, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 4, 3, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 5, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 5, 2, 3, 1], [1, 1, 1, 0]]} "Class ", 4064, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 4, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 4, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {}], [[4, 2, 3, 1, 5], {1, 2, 3}, {}], [[5, 2, 3, 1, 4], {2, 3}, {}], [[5, 2, 4, 1, 3], {2, 3}, {}], [[5, 3, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1507, 9086, 61340, 458167, 3750478, 33385787, 321075365, 3317443919, 36648368431, 431051461702, 5377917092245, 70937789043501, 986371129061998, 14419552529952888] "" "Class ", 4065, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 4, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 4, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 283, 1483, 8728, 56767, 403063, 3094959, 25508734, 224290352, 2093126715, 20642254800, 214325968014, 2335289013721, 26626838763877, 316897638167177, 3927939853155133] "" "Class ", 4066, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {}, {[1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {}, {}], [[3, 4, 1, 2, 5], {2, 3, 4}, {[1, 0, 0, 0, 0, 0]}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {2, 3, 4}, {[1, 0, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {3}, {[1, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {3}, {[1, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 281, 1456, 8452, 54128, 377958, 2851288, 23071081, 199040995, 1821794397, 17615446641, 179280975542, 1914412578157, 21388502635935, 249396598683479, 3028335766532997] "" "Class ", 4067, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 4, 3, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]} "Class ", 4068, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 4, 3, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 5, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 0, 1, 1]]} "Class ", 4069, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 4, 3, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 5, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 5, 2, 3, 1], [1, 0, 1, 1]]} "Class ", 4070, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 4, 3, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 5, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]} "Class ", 4071, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 2, 3, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 4, 3, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 5, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 4, 1, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 5, 2, 3, 1], [1, 1, 1, 1]]} "Class ", 4072, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 2, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 4, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 4, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 2, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 4, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 4, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {}], [[4, 2, 3, 1, 5], {1, 2, 3}, {}], [[5, 2, 3, 1, 4], {1, 2, 3}, {}], [[5, 2, 4, 1, 3], {1, 2}, {}], [[5, 3, 4, 1, 2], {1, 2}, {}], [[5, 3, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 287, 1559, 9684, 67636, 524810, 4479508, 41713098, 420797522, 4571446617, 53210618324, 660651019357, 8715150337215, 121730997119590, 1794768862628915, 27854302791589702] "" "Class ", 4073, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 4, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 4, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 283, 1508, 9202, 63023, 478317, 3986960, 36209506, 355845107, 3762184228, 42578837995, 513604354274, 6577810936819, 89141106337474, 1274389899783729, 19167805172214959] "" "Class ", 4074, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 4, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]} "Class ", 4075, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 2, 3, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 4, 3, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 4, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 4, 2, 3, 1], [1, 1, 0, 0]]} "Class ", 4076, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 2, 3, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 4, 3, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 4, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 4, 2, 3, 1], [0, 0, 1, 0]]} "Class ", 4077, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 4, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 1, 0]]} "Class ", 4078, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 4, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 1, 0]]} "Class ", 4079, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 2, 3, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 4, 3, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 4, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 4, 2, 3, 1], [1, 1, 1, 0]]} "Class ", 4080, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 2, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 4, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 2, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 4, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {}], [[4, 2, 3, 1, 5], {1, 2, 3}, {}], [[5, 2, 3, 1, 4], {2, 3}, {}], [[5, 2, 4, 1, 3], {2, 3}, {}], [[5, 3, 4, 1, 2], {2, 3}, {}], [[5, 3, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 283, 1496, 8977, 60243, 446896, 3629585, 32029675, 305131817, 3120711558, 34102330970, 396522040067, 4887752146169, 63664388085952, 873706876716006, 12600304302785632] "" "Class ", 4081, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 279, 1428, 8175, 51581, 354534, 2630684, 20924059, 177365830, 1594436791, 15136821449, 151209821734, 1584422648325, 17365982116195, 198606425057355, 2364807551475130] "" "Class ", 4082, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]} "Class ", 4083, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]} "Class ", 4084, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 2, 3, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 4, 3, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 4, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 4, 2, 3, 1], [0, 0, 1, 1]]} "Class ", 4085, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 4, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 1, 1]]} "Class ", 4086, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 4, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 1, 1]]} "Class ", 4087, " is:" {{[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 2, 3, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 4, 3, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 3, 2, 4, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 4, 2, 3, 1], [1, 1, 1, 1]]} "Class ", 4088, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 4, 3], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 4, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {1}, {}], [[4, 3, 1, 2, 5], {1, 2, 3}, {}], [[5, 3, 1, 2, 4], {1, 2, 3}, {}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 289, 1573, 9796, 68681, 535028, 4584380, 42850850, 433906296, 4731706366, 55284563621, 688999893668, 9123540672438, 127917866281033, 1893128378099473, 29492073667056032] "" "Class ", 4089, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 4, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 4, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {[0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 288, 1557, 9619, 66805, 515045, 4364418, 40316344, 403194884, 4339927366, 50024959849, 614772640249, 8023890616272, 110843270071857, 1615695616236387, 24782424387482740] "" "Class ", 4090, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 2, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 4, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 4, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 4, 5, 2, 1], [0, 1, 0, 0]]} "Class ", 4091, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 2, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 4, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 4, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 4, 5, 2, 1], [1, 1, 0, 0]]} "Class ", 4092, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {3}, {}], [[2, 1, 3, 4, 5], {3}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3}, {}], [[3, 1, 2, 4, 5], {3}, {}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3}, {}], [[3, 2, 1, 4, 5], {3}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 4, 5, 1], {3, 4}, {}], [[4, 1, 2, 3, 5], {3}, {}], [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 3, 5, 2], {1, 2, 3}, {}], [[4, 2, 1, 3, 5], {3}, {}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 3, 5, 1], {3, 4}, {}], [[4, 3, 1, 2, 5], {3}, {}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {3, 4}, {}], [[5, 1, 2, 3, 4], {3}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3}, {}], [[5, 2, 1, 3, 4], {3}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {3, 4}, {}], [[5, 3, 1, 2, 4], {3}, {}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {3, 4}, {}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 285, 1521, 9254, 63213, 478792, 3980804, 36032796, 352654752, 3710240678, 41752701737, 500390467092, 6362347228570, 85534665976190, 1212203672970876, 18061123999918576] "" "Class ", 4093, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {[0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [[2, 1, 3, 4, 5], {3}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3}, {}], [[3, 1, 2, 4, 5], {3}, {}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3}, {}], [[3, 2, 1, 4, 5], {3}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 4, 5, 1], {3, 4}, {}], [[4, 1, 2, 3, 5], {3}, {}], [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 3, 5, 2], {1, 2, 3}, {}], [[4, 2, 1, 3, 5], {3}, {}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 3, 5, 1], {3, 4}, {}], [[4, 3, 1, 2, 5], {1, 3}, {[0, 0, 1, 0, 0, 0]}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {3, 4}, {}], [[5, 1, 2, 3, 4], {3}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3}, {}], [[5, 2, 1, 3, 4], {3}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {3, 4}, {}], [[5, 3, 1, 2, 4], {1, 3}, {[0, 0, 1, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {3, 4}, {}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 3}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1504, 9040, 60732, 450439, 3651934, 32105419, 304016226, 3083344304, 33331078568, 382433746468, 4640342061512, 59350953760993, 797891674908239, 11245678552263602] "" "Class ", 4094, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 2, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 4, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 4, 5, 2, 1], [0, 1, 1, 0]]} "Class ", 4095, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 2, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 4, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 4, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 4, 5, 2, 1], [1, 1, 1, 0]]} "Class ", 4096, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {2}, {}], [[4, 3, 1, 2, 5], {1, 2, 3}, {}], [[5, 3, 1, 2, 4], {2, 3}, {}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 286, 1529, 9290, 63164, 474790, 3909019, 34979899, 338030097, 3508167505, 38914656146, 459449953471, 5752469674272, 76127372913647, 1061763780332010, 15565874738338104] "" "Class ", 4097, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {[0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 285, 1510, 9047, 60265, 440988, 3511256, 30194246, 278701838, 2747061063, 28786913754, 319494808076, 3743048415151, 46153039186202, 597377254386009, 8097447243797885] "" "Class ", 4098, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 2, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 4, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 4, 5, 2, 1], [0, 1, 0, 1]]} "Class ", 4099, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 2, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 4, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 4, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 4, 5, 2, 1], [1, 1, 0, 1]]} "Class ", 4100, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 2, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 4, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[3, 4, 5, 2, 1], [0, 0, 1, 1]]} "Class ", 4101, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {}, {}], [[3, 2, 4, 1], {}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {[0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [[2, 1, 3, 4, 5], {3}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3}, {}], [[3, 1, 4, 5, 2], {1, 2, 3}, {}], [[3, 2, 1, 4, 5], {3}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 4, 1, 5], {3}, {}], [[3, 2, 4, 5, 1], {3}, {}], [[3, 2, 5, 1, 4], {1, 2}, {}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {1, 2}, {}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {3}, {}], [[4, 3, 5, 1, 2], {1, 2}, {[0, 0, 1, 0, 0, 0]}], [[4, 3, 5, 2, 1], {4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 282, 1467, 8535, 54549, 377704, 2803284, 22118864, 184343047, 1614333907, 14791119212, 141284497983, 1402673019286, 14436350918719, 153680481541310, 1688822035721621] "" "Class ", 4102, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 2, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 4, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 4, 5, 2, 1], [0, 1, 1, 1]]} "Class ", 4103, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 4, 5, 2, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 4, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 4, 5, 2, 1], [1, 1, 1, 1]]} "Class ", 4104, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 3, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 3, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 292, 1576, 9740, 67682, 522157, 4427769, 40925550, 409511145, 4410271323, 50861937594, 625368693140, 8166100805705, 112859919079333, 1645825012584089, 25255451056013188] "" "Class ", 4105, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 3, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 5, 2, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 1, 4, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 3, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 1, 3, 2], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 3, 5, 2, 1], [0, 1, 0, 0]]} "Class ", 4106, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 3, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 5, 2, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 1, 4, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 3, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 1, 3, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 3, 5, 2, 1], [1, 1, 0, 0]]} "Class ", 4107, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [[2, 1, 3, 4, 5], {3}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3}, {}], [[3, 1, 2, 4, 5], {3}, {}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3}, {}], [[3, 2, 1, 4, 5], {3}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 4, 5, 1], {3, 4}, {}], [[4, 1, 2, 3, 5], {3}, {}], [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 3, 5, 2], {1, 2, 3}, {}], [[4, 2, 1, 3, 5], {3}, {}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 3, 5, 1], {3, 4}, {}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {3, 4}, {}], [[5, 1, 2, 3, 4], {3}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3}, {}], [[5, 2, 1, 3, 4], {3}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {3, 4}, {}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 292, 1554, 9345, 62670, 463578, 3747297, 32838271, 309868130, 3130633427, 33700706066, 384931466712, 4648215104503, 59150506461498, 790985062996501, 11087030423275181] "" "Class ", 4108, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 5, 2, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 1, 4, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 3, 5, 2, 1], [0, 1, 1, 0]]} "Class ", 4109, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 5, 2, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 1, 4, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 3, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 3, 5, 2, 1], [1, 1, 1, 0]]} "Class ", 4110, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 292, 1563, 9484, 64095, 476288, 3855049, 33728843, 316982481, 3182887087, 33992972037, 384622280833, 4594799930477, 57779099576839, 762742253884788, 10544857581933701] "" "Class ", 4111, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 5, 2, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 1, 4, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 3, 5, 2, 1], [0, 1, 0, 1]]} "Class ", 4112, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 5, 2, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 1, 4, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 3, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 1, 3, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 3, 5, 2, 1], [1, 1, 0, 1]]} "Class ", 4113, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 3, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 3, 4], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {}, {}], [[3, 2, 4, 1], {}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [[2, 1, 3, 4, 5], {3}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3}, {}], [[3, 1, 4, 5, 2], {1, 2, 3}, {}], [[3, 2, 1, 4, 5], {3}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 4, 1, 5], {3}, {}], [[3, 2, 4, 5, 1], {3}, {}], [[3, 2, 5, 1, 4], {1, 2}, {}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {1, 2}, {}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {3}, {}], [[4, 3, 5, 1, 2], {4}, {[0, 1, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 63, 292, 1546, 9142, 59318, 416516, 3130584, 24969550, 209906019, 1849775312, 17014007123, 162759419841, 1614558961425, 16566955616065, 175460071012084, 1914469400543660] "" "Class ", 4114, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 3, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 5, 2, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 1, 4, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 3, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 1, 3, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 3, 5, 2, 1], [0, 1, 1, 1]]} "Class ", 4115, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 1, 3, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 3, 5, 2, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 3, 1, 4, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 5, 3, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 1, 3, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 3, 5, 2, 1], [1, 1, 1, 1]]} "Class ", 4116, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {}, {}], [[4, 3, 2, 1, 5], {1, 2, 3}, {}], [[5, 3, 2, 1, 4], {1, 2, 3}, {}], [[5, 4, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {1, 2, 3}, {}], [[5, 4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 290, 1582, 9863, 69225, 539891, 4631594, 43344682, 439440294, 4797862433, 56125325612, 700323950222, 9284705886521, 130334957900070, 1931233431081993, 30122083893576425] "" "Class ", 4117, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 288, 1560, 9643, 67044, 517652, 4393844, 40664151, 407507330, 4396020404, 50790535355, 625731305619, 8188230520853, 113421839735744, 1657969055522390, 25505524819275398] "" "Class ", 4118, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 2, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 4, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 5, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 5, 4, 2, 1], [0, 1, 0, 0]]} "Class ", 4119, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 2, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 4, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 5, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 5, 4, 2, 1], [1, 1, 0, 0]]} "Class ", 4120, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {}, {}], [[2, 1, 3, 4, 5], {3}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3}, {}], [[3, 1, 2, 4, 5], {3}, {}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3}, {}], [[3, 2, 1, 4, 5], {3}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 4, 5, 1], {3, 4}, {}], [[4, 1, 2, 3, 5], {3}, {}], [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 3, 5, 2], {1, 2, 3}, {}], [[4, 2, 1, 3, 5], {3}, {}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 3, 5, 1], {3, 4}, {}], [[4, 3, 1, 2, 5], {3}, {}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 1, 5], {3}, {}], [[4, 3, 2, 5, 1], {3, 4}, {}], [[5, 1, 2, 3, 4], {3}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3}, {}], [[5, 2, 1, 3, 4], {3}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {3, 4}, {}], [[5, 3, 1, 2, 4], {3}, {}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {3}, {}], [[5, 3, 2, 4, 1], {3, 4}, {}], [[5, 4, 1, 2, 3], {3}, {}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {3}, {}], [[5, 4, 3, 1, 2], {3}, {}], [[5, 4, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 286, 1539, 9447, 65139, 498304, 4186078, 38305350, 379209099, 4037608766, 46006357901, 558545625282, 7197404515043, 98105128085966, 1410223162393856, 21319728397964831] "" "Class ", 4121, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {1}, {[0, 0, 1, 0, 0]}], [[2, 1, 3, 4, 5], {3}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3}, {}], [[3, 1, 2, 4, 5], {3}, {}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3}, {}], [[3, 2, 1, 4, 5], {3}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 4, 5, 1], {3, 4}, {}], [[4, 1, 2, 3, 5], {3}, {}], [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 3, 5, 2], {1, 2, 3}, {}], [[4, 2, 1, 3, 5], {3}, {}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 3, 5, 1], {3, 4}, {}], [[4, 3, 1, 2, 5], {3}, {}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {3, 4}, {}], [[5, 1, 2, 3, 4], {3}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3}, {}], [[5, 2, 1, 3, 4], {3}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {3, 4}, {}], [[5, 3, 1, 2, 4], {3}, {}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {3, 4}, {}], [[5, 4, 1, 2, 3], {3}, {}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 3}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 285, 1521, 9216, 62461, 467851, 3834408, 34114746, 327295057, 3366786857, 36953812919, 430958962118, 5320332072797, 69302840202051, 949758086960334, 13658320061721187] "" "Class ", 4122, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 2, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 4, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 5, 4, 2, 1], [0, 1, 1, 0]]} "Class ", 4123, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 2, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 4, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 5, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 5, 4, 2, 1], [1, 1, 1, 0]]} "Class ", 4124, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {}, {}], [[4, 3, 2, 1, 5], {1, 2, 3}, {}], [[5, 3, 2, 1, 4], {2, 3}, {}], [[5, 4, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {2, 3}, {}], [[5, 4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 288, 1556, 9579, 66214, 507403, 4269111, 39123687, 387896999, 4137004509, 47227165773, 574580748503, 7421796132042, 101436977798277, 1462518397992493, 22184310407965828] "" "Class ", 4125, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 286, 1530, 9284, 62970, 471373, 3857189, 34241152, 327639935, 3361195750, 36799316979, 428242821068, 5278572535430, 68700587909806, 941471212020022, 13550741557657626] "" "Class ", 4126, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 2, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 4, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 5, 4, 2, 1], [0, 1, 0, 1]]} "Class ", 4127, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 2, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 4, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 5, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 5, 4, 2, 1], [1, 1, 0, 1]]} "Class ", 4128, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 2, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 4, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 5, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[3, 5, 4, 2, 1], [0, 0, 1, 1]]} "Class ", 4129, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[3, 5, 4, 2, 1], [1, 0, 1, 1]]} "Class ", 4130, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 2, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 4, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 5, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[3, 5, 4, 2, 1], [0, 1, 1, 1]]} "Class ", 4131, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 5, 4, 2, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2, 4, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 5, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 2, 1, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[3, 5, 4, 2, 1], [1, 1, 1, 1]]} "Class ", 4132, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 3, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 3, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {1}, {}], [[4, 3, 1, 2, 5], {1, 2, 3}, {}], [[5, 3, 1, 2, 4], {1, 2, 3}, {}], [[5, 4, 1, 2, 3], {1, 2, 3}, {}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 288, 1573, 9819, 68889, 536990, 4604519, 43073698, 436521532, 4764074027, 55707592830, 694831554676, 9208176151067, 129208568369081, 1913771468750824, 29837691630813486] "" "Class ", 4133, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 3, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 3, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {[1, 0, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 285, 1535, 9464, 65579, 504504, 4266140, 39328552, 392569925, 4218001546, 48536874536, 595520582001, 7760637995134, 107048842957372, 1558189211449520, 23868108303131712] "" "Class ", 4134, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 2, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 4, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 3, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 3, 4, 2, 1], [0, 1, 0, 0]]} "Class ", 4135, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 2, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 4, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 3, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 3, 4, 2, 1], [1, 1, 0, 0]]} "Class ", 4136, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {3}, {}], [[2, 1, 3, 4, 5], {3}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3}, {}], [[3, 1, 2, 4, 5], {3}, {}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3}, {}], [[3, 2, 1, 4, 5], {3}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 4, 5, 1], {3, 4}, {}], [[4, 1, 2, 3, 5], {3}, {}], [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 3, 5, 2], {1, 2, 3}, {}], [[4, 2, 1, 3, 5], {3}, {}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 3, 5, 1], {3, 4}, {}], [[4, 3, 1, 2, 5], {3}, {}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {3, 4}, {}], [[5, 1, 2, 3, 4], {3}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3}, {}], [[5, 2, 1, 3, 4], {3}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {3, 4}, {}], [[5, 3, 1, 2, 4], {3}, {}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {3, 4}, {}], [[5, 4, 1, 2, 3], {3}, {}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 283, 1507, 9187, 62901, 477393, 3977397, 36084063, 354056867, 3735470340, 42164576666, 506970915240, 6468262868992, 87274863465067, 1241581029300379, 18572401088850217] "" "Class ", 4137, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {[1, 0, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [[2, 1, 3, 4, 5], {3}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3}, {}], [[3, 1, 2, 4, 5], {3}, {}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3}, {}], [[3, 2, 1, 4, 5], {3}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 4, 5, 1], {3, 4}, {}], [[4, 1, 2, 3, 5], {3}, {}], [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 3, 5, 2], {1, 2, 3}, {}], [[4, 2, 1, 3, 5], {3}, {}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 3, 5, 1], {3, 4}, {}], [[4, 3, 1, 2, 5], {3}, {[1, 0, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {3, 4}, {}], [[5, 1, 2, 3, 4], {3}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3}, {}], [[5, 2, 1, 3, 4], {3}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {3, 4}, {}], [[5, 3, 1, 2, 4], {3}, {[1, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {3, 4}, {}], [[5, 4, 1, 2, 3], {3}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 281, 1471, 8762, 58406, 429938, 3460000, 30198563, 283959505, 2860505330, 30721442270, 350290294326, 4224811969766, 53724686169748, 718255883782118, 10069473565571541] "" "Class ", 4138, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 2, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 4, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 3, 4, 2, 1], [0, 1, 1, 0]]} "Class ", 4139, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 2, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 4, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 3, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 3, 4, 2, 1], [1, 1, 1, 0]]} "Class ", 4140, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {2}, {}], [[4, 3, 1, 2, 5], {1, 2, 3}, {}], [[5, 3, 1, 2, 4], {2, 3}, {}], [[5, 4, 1, 2, 3], {2, 3}, {}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 286, 1544, 9494, 65391, 499333, 4186301, 38215682, 377351737, 4007402503, 45543240449, 551510201143, 7089311527168, 96407402774215, 1382817746719636, 20863830501118550] "" "Class ", 4141, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {[1, 0, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 283, 1499, 9010, 60307, 444063, 3564398, 30950890, 288890299, 2882885726, 30616353650, 344649546911, 4098129502820, 51314659385149, 674772064496843, 9295419570773829] "" "Class ", 4142, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 2, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 4, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 3, 4, 2, 1], [0, 1, 0, 1]]} "Class ", 4143, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 2, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 4, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 3, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 3, 4, 2, 1], [1, 1, 0, 1]]} "Class ", 4144, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 4, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 3, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 3, 4, 2, 1], [0, 0, 1, 1]]} "Class ", 4145, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]} "Class ", 4146, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 2, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 4, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 3, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 3, 4, 2, 1], [0, 1, 1, 1]]} "Class ", 4147, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 3, 2, 4, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 4, 3, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 2, 3, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]} "Class ", 4148, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {}, {}], [[4, 3, 2, 1, 5], {1, 2, 3}, {}], [[5, 3, 2, 1, 4], {1, 2, 3}, {}], [[5, 4, 2, 1, 3], {1, 2, 3}, {}], [[5, 4, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 289, 1577, 9833, 68995, 537922, 4613057, 43156468, 437384385, 4773816928, 55825422572, 696348950537, 9228918107420, 129508489737191, 1918345245597322, 29911052705353378] "" "Class ", 4149, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 288, 1560, 9643, 67044, 517652, 4393844, 40664151, 407507330, 4396020404, 50790535355, 625731305619, 8188230520853, 113421839735744, 1657969055522390, 25505524819275398] "" "Class ", 4150, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {}, {}], [[3, 4, 1, 2, 5], {2, 3, 4}, {}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {2, 3, 4}, {}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {}], [[4, 5, 1, 3, 2], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3}, {}], [[4, 5, 3, 1, 2], {3}, {}], [[4, 5, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 285, 1529, 9370, 64512, 492726, 4132396, 37748406, 373023144, 3964403790, 45086120928, 546298073078, 7025362571236, 95561556360908, 1370744288154617, 20677943122391404] "" "Class ", 4151, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 2, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 5, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 5, 3, 2, 1], [1, 1, 0, 0]]} "Class ", 4152, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {}, {}], [[2, 1, 3, 4, 5], {3}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3}, {}], [[3, 1, 2, 4, 5], {3}, {}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3}, {}], [[3, 2, 1, 4, 5], {3}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 4, 5, 1], {3, 4}, {}], [[4, 1, 2, 3, 5], {3}, {}], [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 3, 5, 2], {1, 2, 3}, {}], [[4, 2, 1, 3, 5], {3}, {}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 3, 5, 1], {3, 4}, {}], [[4, 3, 1, 2, 5], {3}, {}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 1, 5], {3}, {}], [[4, 3, 2, 5, 1], {3, 4}, {}], [[5, 1, 2, 3, 4], {3}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3}, {}], [[5, 2, 1, 3, 4], {3}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {3, 4}, {}], [[5, 3, 1, 2, 4], {3}, {}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {3}, {}], [[5, 3, 2, 4, 1], {3, 4}, {}], [[5, 4, 1, 2, 3], {3}, {}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {3}, {}], [[5, 4, 2, 3, 1], {3}, {}], [[5, 4, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 285, 1531, 9401, 64817, 495723, 4164313, 38108777, 377324459, 4018630630, 45806086448, 556346463822, 7172520537348, 97818600859735, 1406934712679043, 21283587251414669] "" "Class ", 4153, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {3}, {[0, 1, 0, 0, 0]}], [[2, 1, 3, 4, 5], {3}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3}, {}], [[3, 1, 2, 4, 5], {3}, {}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3}, {}], [[3, 2, 1, 4, 5], {3}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 4, 5, 1], {3, 4}, {}], [[4, 1, 2, 3, 5], {3}, {}], [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 3, 5, 2], {1, 2, 3}, {}], [[4, 2, 1, 3, 5], {3}, {}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 3, 5, 1], {3, 4}, {}], [[4, 3, 1, 2, 5], {3}, {}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {3, 4}, {}], [[5, 1, 2, 3, 4], {3}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3}, {}], [[5, 2, 1, 3, 4], {3}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {3, 4}, {}], [[5, 3, 1, 2, 4], {3}, {}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {3, 4}, {}], [[5, 4, 1, 2, 3], {3}, {}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1511, 9135, 61754, 461423, 3773227, 33495603, 320648535, 3291269505, 36047065314, 419483739736, 5167646203934, 67171620988164, 918618655738242, 13183001084851384] "" "Class ", 4154, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 1, 0]]} "Class ", 4155, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 2, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 5, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 5, 3, 2, 1], [1, 1, 1, 0]]} "Class ", 4156, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {}, {}], [[4, 3, 2, 1, 5], {1, 2, 3}, {}], [[5, 3, 2, 1, 4], {2, 3}, {}], [[5, 4, 2, 1, 3], {2, 3}, {}], [[5, 4, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 288, 1563, 9677, 67310, 519528, 4405423, 40712584, 407260730, 4384147250, 50534283663, 620974007265, 8103523530498, 111919369566334, 1630964514603476, 25009419424306557] "" "Class ", 4157, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 287, 1545, 9457, 64848, 491758, 4082734, 36815638, 358158140, 3737950823, 41650470086, 493421548287, 6192134755714, 82050948155720, 1144715304866552, 16771087916420136] "" "Class ", 4158, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {}, {[1, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {2, 3, 4}, {}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {2, 3, 4}, {}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {}], [[4, 5, 1, 3, 2], {3}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3}, {[1, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {3}, {[1, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1512, 9153, 61908, 461950, 3765129, 33252879, 316141137, 3217436695, 34884960392, 401299814954, 4880152912921, 62538830130750, 842152805135820, 11886654546095919] "" "Class ", 4159, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 2, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 5, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 5, 3, 2, 1], [1, 1, 0, 1]]} "Class ", 4160, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 5, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 0, 1, 1]]} "Class ", 4161, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 5, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[4, 5, 3, 2, 1], [1, 0, 1, 1]]} "Class ", 4162, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 5, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]} "Class ", 4163, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[4, 5, 3, 2, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 5, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[4, 5, 3, 2, 1], [1, 1, 1, 1]]} "Class ", 4164, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {}, {}], [[4, 3, 2, 1, 5], {1, 2, 3}, {}], [[5, 3, 2, 1, 4], {1, 2, 3}, {}], [[5, 4, 2, 1, 3], {1, 2, 3}, {}], [[5, 4, 3, 1, 2], {1, 2, 3}, {}], [[5, 4, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 289, 1582, 9879, 69357, 541205, 4645564, 43501981, 441303032, 4821098162, 56431346122, 704569139748, 9346638381116, 131283732983128, 1946468977746268, 30378089311784796] "" "Class ", 4165, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 285, 1539, 9524, 66178, 510405, 4328867, 40034580, 400936968, 4322657207, 49917205513, 614684922800, 8040278867638, 111329623762089, 1626813463289479, 25018166600578492] "" "Class ", 4166, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]} "Class ", 4167, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 4, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]} "Class ", 4168, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {}, {}], [[2, 1, 3, 4, 5], {3}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3}, {}], [[3, 1, 2, 4, 5], {3}, {}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3}, {}], [[3, 2, 1, 4, 5], {3}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 4, 5, 1], {3, 4}, {}], [[4, 1, 2, 3, 5], {3}, {}], [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 3, 5, 2], {1, 2, 3}, {}], [[4, 2, 1, 3, 5], {3}, {}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 3, 5, 1], {3, 4}, {}], [[4, 3, 1, 2, 5], {3}, {}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 1, 5], {3}, {}], [[4, 3, 2, 5, 1], {3, 4}, {}], [[5, 1, 2, 3, 4], {3}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3}, {}], [[5, 2, 1, 3, 4], {3}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {3, 4}, {}], [[5, 3, 1, 2, 4], {3}, {}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {3}, {}], [[5, 3, 2, 4, 1], {3, 4}, {}], [[5, 4, 1, 2, 3], {3}, {}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {3}, {}], [[5, 4, 2, 3, 1], {3}, {}], [[5, 4, 3, 1, 2], {3}, {}], [[5, 4, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 286, 1547, 9562, 66357, 511125, 4326879, 39922534, 398717317, 4285143037, 49308038164, 604793639683, 7876836509134, 108557998681223, 1578370173866747, 24143554916639221] "" "Class ", 4169, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {3}, {[1, 0, 0, 0, 0]}], [[2, 1, 3, 4, 5], {3}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3}, {}], [[3, 1, 2, 4, 5], {3}, {}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3}, {}], [[3, 2, 1, 4, 5], {3}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 4, 5, 1], {3, 4}, {}], [[4, 1, 2, 3, 5], {3}, {}], [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 3, 5, 2], {1, 2, 3}, {}], [[4, 2, 1, 3, 5], {3}, {}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 3, 5, 1], {3, 4}, {}], [[4, 3, 1, 2, 5], {3}, {}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {3, 4}, {}], [[5, 1, 2, 3, 4], {3}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3}, {}], [[5, 2, 1, 3, 4], {3}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {3, 4}, {}], [[5, 3, 1, 2, 4], {3}, {}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {3, 4}, {}], [[5, 4, 1, 2, 3], {3}, {}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {3, 4}, {[1, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 282, 1491, 9006, 60915, 455183, 3723787, 33093375, 317315774, 3263954058, 35840029552, 418323243208, 5170738592170, 67461745664258, 926301470369658, 13350450266101954] "" "Class ", 4170, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 1, 0]]} "Class ", 4171, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 4, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]} "Class ", 4172, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {}, {}], [[4, 3, 2, 1, 5], {1, 2, 3}, {}], [[5, 3, 2, 1, 4], {2, 3}, {}], [[5, 4, 2, 1, 3], {2, 3}, {}], [[5, 4, 3, 1, 2], {2, 3}, {}], [[5, 4, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 288, 1568, 9728, 67761, 524123, 4455751, 41291508, 414288083, 4474019538, 51742857205, 638045174526, 8356437447373, 115843231704283, 1694618051241397, 26087490137706882] "" "Class ", 4173, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 16, 62, 284, 1520, 9281, 63366, 478110, 3950639, 35465926, 343608014, 3572577858, 39670668263, 468495695832, 5862617026615, 77484202993207, 1078475630898965, 15767119770876919] "" "Class ", 4174, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]} "Class ", 4175, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]} "Class ", 4176, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 4, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 4, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]} "Class ", 4177, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]} "Class ", 4178, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 4, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 0]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]} "Class ", 4179, " is:" {{[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 0]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 0]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 0]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 0]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 0]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]} "Class ", 4180, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 5, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1265, 4147, 13798, 46476, 158170, 543050, 1878670, 6542330, 22915999, 80682987, 285378270, 1013564805, 3613262795] "" "Class ", 4181, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1210, 3865, 12482, 40677, 133572, 441468, 1467296, 4900760, 16439370, 55357305, 187050302, 633998079, 2154950454] "" "Class ", 4182, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]} "Class ", 4183, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4, 5], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4, 5], [1, 1, 0, 0]]} "Class ", 4184, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[1, 2, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 5, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1221, 3939, 12886, 42648, 142544, 480459, 1631287, 5574073, 19153815, 66146259, 229452587, 799140681, 2793373937] "" "Class ", 4185, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [ [1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 4186, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 1, 0]]} "Class ", 4187, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4, 5], [1, 1, 1, 0]]} "Class ", 4188, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 5, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1265, 4147, 13798, 46476, 158170, 543050, 1878670, 6542330, 22915999, 80682987, 285378270, 1013564805, 3613262795] "" "Class ", 4189, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1210, 3865, 12482, 40677, 133572, 441468, 1467296, 4900760, 16439370, 55357305, 187050302, 633998079, 2154950454] "" "Class ", 4190, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]} "Class ", 4191, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]} "Class ", 4192, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[1, 2, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 5, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1221, 3939, 12886, 42648, 142544, 480459, 1631287, 5574073, 19153815, 66146259, 229452587, 799140681, 2793373937] "" "Class ", 4193, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [ [1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 4194, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]} "Class ", 4195, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]} "Class ", 4196, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 5, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 3, 5, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]} "Class ", 4197, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 5, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 3, 2, 1], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 3, 5, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 0, 0]]} "Class ", 4198, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 5, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 3, 5, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 1, 0]]} "Class ", 4199, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 5, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 3, 2, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 3, 5, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 1, 0]]} "Class ", 4200, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]} "Class ", 4201, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 3, 2, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 0, 1]]} "Class ", 4202, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 1, 1]]} "Class ", 4203, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 3, 2, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 1, 1]]} "Class ", 4204, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 4, 3, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 2, 4, 5], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 4, 2, 1], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 4, 3, 5], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 4, 3, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 2, 4, 5], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 4, 2, 1], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 4, 3, 5], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4205, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4206, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 4, 3, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 2, 4, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 4, 2, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 4, 3, 5], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 4, 3, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 2, 4, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 4, 2, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 4, 3, 5], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4207, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 4, 3, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 2, 4, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 4, 2, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 4, 3, 5], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 4, 3, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 2, 4, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 4, 2, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 4, 3, 5], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4208, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 2, 4, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 4, 2, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 2, 4, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 4, 2, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4209, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4210, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 2, 4, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 4, 2, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 2, 4, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 4, 2, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4211, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 2, 4, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 2, 4, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4212, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2, 4, 5], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 4, 2, 1], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2, 4, 5], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 4, 2, 1], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4213, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 4, 2, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 4, 2, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4214, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2, 4, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 4, 2, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2, 4, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 4, 2, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4215, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2, 4, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 4, 2, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2, 4, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 4, 2, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4216, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2, 4, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 4, 2, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2, 4, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 4, 2, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4217, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 4, 2, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 4, 2, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4218, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2, 4, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 4, 2, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2, 4, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 4, 2, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4219, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2, 4, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 4, 2, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2, 4, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 4, 2, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4220, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 5, 2, 1], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 5, 2, 1], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4221, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4222, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1, 4, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1, 4, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4223, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1, 4, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 5, 2, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1, 4, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 5, 2, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4224, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 5, 2, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 5, 2, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4225, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4226, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1, 4, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1, 4, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4227, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1, 4, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 5, 2, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1, 4, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 5, 2, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4228, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1, 4, 5], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 5, 2, 1], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1, 4, 5], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 5, 2, 1], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4229, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4230, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1, 4, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1, 4, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4231, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1, 4, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1, 4, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4232, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1, 4, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 5, 2, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1, 4, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 5, 2, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4233, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4234, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1, 4, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1, 4, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4235, " is:" {{[[1, 3, 2], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4236, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 4, 3, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 2, 3, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 4, 3, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 2, 3, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4237, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 4, 3, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 4, 3, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4238, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4239, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4240, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 4, 3, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 2, 3, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 4, 3, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 2, 3, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4241, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 4, 3, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 2, 3, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 4, 3, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 2, 3, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4242, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 4, 3, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 4, 3, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4243, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 4, 3, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 2, 3, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 4, 3, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 2, 3, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4244, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4245, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 4, 3, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 4, 3, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4246, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 2, 5, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 4, 3, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 2, 5, 4], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 2, 5, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 4, 3, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 2, 5, 4], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4247, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 2, 5, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 4, 3, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 2, 3, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 2, 5, 4], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 2, 5, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 4, 3, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 2, 3, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 2, 5, 4], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4248, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 2, 3, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 4, 3, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 2, 4, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 2, 3, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 4, 3, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 2, 4, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4249, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 2, 3, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 4, 3, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 2, 4, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 2, 3, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 4, 3, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 2, 4, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4250, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 2, 3, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 4, 3, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 2, 4, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 2, 3, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 4, 3, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 2, 4, 1], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4251, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 2, 3, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 4, 3, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 2, 4, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 2, 3, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 4, 3, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 2, 4, 1], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4252, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 2, 3, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 4, 3, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 2, 4, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 2, 3, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 4, 3, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 2, 4, 1], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4253, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 2, 3, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 4, 3, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 2, 4, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 2, 3, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 4, 3, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 2, 4, 1], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4254, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 2, 3, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 4, 3, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 2, 4, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 2, 3, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 4, 3, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 2, 4, 1], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4255, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 2, 3, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 4, 3, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 2, 4, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 2, 3, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 4, 3, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 2, 4, 1], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4256, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 2, 3, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 4, 3, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 2, 3, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 4, 3, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4257, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 2, 3, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 4, 3, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 2, 3, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 4, 3, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4258, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 2, 3, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 4, 3, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 2, 3, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 4, 3, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4259, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 2, 3, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 4, 3, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 2, 3, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 4, 3, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4260, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 2, 3, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 4, 3, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 2, 3, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 4, 3, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4261, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 2, 3, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 4, 3, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 2, 3, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 4, 3, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4262, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 2, 3, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 4, 3, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 2, 3, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 4, 3, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4263, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 2, 3, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 4, 3, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 2, 3, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 4, 3, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4264, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 1, 3, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 5, 3, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 1, 4, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 1, 3, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 5, 3, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 1, 4, 2], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4265, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 1, 3, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 5, 3, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 1, 4, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 1, 3, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 5, 3, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 1, 4, 2], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4266, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 1, 3, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 5, 3, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 1, 4, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 1, 3, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 5, 3, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 1, 4, 2], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4267, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 1, 3, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 5, 3, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 1, 4, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 1, 3, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 5, 3, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 1, 4, 2], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4268, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 1, 3, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 5, 3, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 1, 2, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 1, 3, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 5, 3, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 1, 2, 4], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4269, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 1, 3, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 5, 3, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 1, 2, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 1, 3, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 5, 3, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 1, 2, 4], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4270, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 1, 3, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 5, 3, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 1, 2, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 1, 3, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 5, 3, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 1, 2, 4], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4271, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 1, 3, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 5, 3, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 1, 2, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 1, 3, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 5, 3, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 3, 1, 2, 4], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4272, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 2, 3, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 4, 2, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 2, 4, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 4, 3, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 2, 3, 5], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 2, 3, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 4, 2, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 2, 4, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 4, 3, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 2, 3, 5], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4273, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 2, 3, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 4, 2, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 2, 4, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 4, 3, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 2, 3, 5], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 2, 3, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 4, 2, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 2, 4, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 4, 3, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 2, 3, 5], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4274, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 2, 3, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 4, 2, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 2, 4, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 4, 3, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 2, 3, 5], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 2, 3, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 4, 2, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 2, 4, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 4, 3, 1], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 2, 3, 5], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4275, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 2, 3, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 4, 2, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 2, 4, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 4, 3, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 2, 3, 5], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 2, 3, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 4, 2, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 2, 4, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 4, 3, 1], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 2, 3, 5], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4276, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 4, 2, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 2, 4, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 4, 3, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 4, 2, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 2, 4, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 4, 3, 1], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4277, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 4, 2, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 2, 4, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 4, 3, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 4, 2, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 2, 4, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 4, 3, 1], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4278, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 4, 2, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 2, 4, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 4, 3, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 4, 2, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 2, 4, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 4, 3, 1], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4279, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 4, 2, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 2, 4, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 4, 3, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 4, 2, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 2, 4, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 4, 3, 1], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4280, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 2, 5, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 4, 2, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 2, 4, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 4, 1, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 2, 5, 3], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 2, 5, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 4, 2, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 2, 4, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 4, 1, 3], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 2, 5, 3], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4281, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 2, 5, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 4, 2, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 2, 4, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 4, 1, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 2, 5, 3], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 2, 5, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 4, 2, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 2, 4, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 4, 1, 3], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 2, 5, 3], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4282, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 2, 5, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 4, 2, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 2, 4, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 4, 1, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 2, 5, 3], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 2, 5, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 4, 2, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 2, 4, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 4, 1, 3], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 2, 5, 3], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4283, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 2, 5, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 4, 2, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 2, 4, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 4, 1, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 2, 5, 3], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 2, 5, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 4, 2, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 2, 4, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 4, 1, 3], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 2, 5, 3], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4284, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 3, 2, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 3, 4, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 3, 4, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 3, 2, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 3, 4, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 3, 4, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4285, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 3, 4, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 3, 4, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 3, 4, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 3, 4, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4286, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 3, 2, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 3, 4, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 3, 4, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 3, 2, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 3, 4, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 3, 4, 1], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4287, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 3, 2, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 3, 4, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 3, 4, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 3, 2, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 3, 4, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 3, 4, 1], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4288, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 3, 2, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 3, 4, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 3, 4, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 3, 2, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 3, 4, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 3, 4, 1], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4289, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 3, 2, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 3, 4, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 3, 4, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 3, 2, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 3, 4, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 3, 4, 1], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4290, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 3, 2, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 3, 4, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 3, 4, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 3, 2, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 3, 4, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 3, 4, 1], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4291, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 3, 2, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 3, 4, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 3, 4, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 3, 2, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 3, 4, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 3, 4, 1], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4292, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 3, 2, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 3, 4, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 3, 1, 4], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 3, 2, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 3, 4, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 3, 1, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4293, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 3, 2, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 3, 4, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 3, 1, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 3, 2, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 3, 4, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 3, 1, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4294, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 3, 2, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 3, 4, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 3, 1, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 3, 2, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 3, 4, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 3, 1, 4], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4295, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 3, 2, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 3, 4, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 3, 1, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 3, 2, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 3, 4, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 3, 1, 4], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4296, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 3, 2, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 3, 4, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 3, 1, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 3, 2, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 3, 4, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 3, 1, 4], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4297, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 3, 2, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 3, 4, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 3, 1, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 3, 2, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 3, 4, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 3, 1, 4], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4298, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 3, 2, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 3, 4, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 3, 1, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 3, 2, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 3, 4, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 3, 1, 4], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4299, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 3, 2, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 3, 4, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 3, 1, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 3, 2, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 3, 4, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 3, 1, 4], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4300, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 5, 4, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 5, 4, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4301, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 1, 2, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 5, 4, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 1, 2, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 5, 4, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4302, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 1, 2, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 5, 4, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 1, 2, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 5, 4, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4303, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 1, 2, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 5, 4, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 1, 2, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 5, 4, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4304, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 1, 2, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 5, 4, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 1, 2, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 5, 4, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4305, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 1, 2, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 5, 4, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 1, 2, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 5, 4, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4306, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 1, 2, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 5, 4, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 1, 2, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 5, 4, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4307, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 1, 2, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 5, 4, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 1, 2, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 5, 4, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4308, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 1, 2, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 5, 4, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 1, 2, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 5, 4, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4309, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 1, 2, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 5, 4, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 1, 2, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 5, 4, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4310, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 1, 2, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 5, 4, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 1, 2, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 5, 4, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4311, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 1, 2, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 5, 4, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 1, 2, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 5, 4, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4312, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 1, 2, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 5, 4, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 1, 2, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 5, 4, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4313, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 1, 2, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 5, 4, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 1, 2, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 5, 4, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4314, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 1, 2, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 5, 4, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 1, 2, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 5, 4, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4315, " is:" {{[[1, 3, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 1, 2, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 5, 4, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 1, 2, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 5, 4, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4316, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 1, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 1, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4317, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 1, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 5, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 1, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 5, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4318, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 1, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 5, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 1, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 5, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4319, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 1, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 5, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 1, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 5, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4320, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 1, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 5, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 1, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 5, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4321, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 1, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 5, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 1, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 5, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4322, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 1, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 5, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 1, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 5, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4323, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 1, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 5, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 1, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 5, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4324, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 4, 1, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 2, 5, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 4, 1, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 2, 5, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4325, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 4, 1, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 2, 5, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 4, 1, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 2, 5, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4326, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 4, 1, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 2, 5, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 4, 1, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 2, 5, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4327, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 4, 1, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 4, 1, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4328, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 3, 1, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 3, 5, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 3, 4, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 3, 1, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 3, 5, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 3, 4, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4329, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 3, 1, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 3, 5, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 3, 4, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 3, 1, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 3, 5, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 3, 4, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4330, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 3, 1, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 3, 5, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 3, 4, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 3, 1, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 3, 5, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 3, 4, 2], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4331, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 3, 1, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 3, 5, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 3, 4, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 3, 1, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 3, 5, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 3, 4, 2], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4332, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 3, 1, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 3, 5, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 3, 1, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 3, 5, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4333, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 3, 1, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 3, 5, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 3, 1, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 3, 5, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4334, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 3, 1, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 3, 5, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 3, 1, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 3, 5, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4335, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 3, 1, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 3, 5, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 3, 1, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 3, 5, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4336, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 3, 1, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 3, 5, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 3, 2, 4], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 3, 1, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 3, 5, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 3, 2, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4337, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 3, 1, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 3, 5, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 3, 2, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 3, 1, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 3, 5, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 3, 2, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4338, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 3, 1, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 3, 5, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 3, 2, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 3, 1, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 3, 5, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 3, 2, 4], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4339, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 3, 1, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 3, 5, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 3, 2, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 3, 1, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 3, 5, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 3, 2, 4], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4340, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 3, 1, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 3, 5, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 3, 1, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 3, 5, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4341, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 3, 1, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 3, 5, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 3, 1, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 3, 5, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4342, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 3, 1, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 3, 5, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 3, 1, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 3, 5, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4343, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 3, 1, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 3, 5, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 3, 1, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 3, 5, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4344, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 2, 1, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 4, 5, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 2, 1, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 4, 5, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4345, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 2, 1, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 4, 5, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 2, 1, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 4, 5, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4346, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 2, 1, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 4, 5, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 2, 1, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 4, 5, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4347, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 2, 1, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 4, 5, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 2, 1, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 4, 5, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4348, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 2, 1, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 4, 5, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 2, 1, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 4, 5, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4349, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 2, 1, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 4, 5, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 2, 1, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 4, 5, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4350, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 2, 1, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 4, 5, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 2, 1, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 4, 5, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4351, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 2, 1, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 4, 5, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 2, 1, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 4, 5, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4352, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4353, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4354, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 2, 1, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 4, 5, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 2, 1, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 4, 5, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4355, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 2, 1, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 4, 5, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 2, 1, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 4, 5, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4356, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4357, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 2, 1, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 2, 1, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4358, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 2, 1, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 4, 5, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 2, 1, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 4, 5, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4359, " is:" {{[[1, 3, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 4, 5, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 4, 5, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4360, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 4, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1265, 4148, 13808, 46542, 158534, 544869, 1887212, 6580775, 23083823, 81399079, 288380766, 1025982051, 3664054185] "" "Class ", 4361, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1211, 3875, 12548, 41040, 135370, 449791, 1504057, 5057668, 17092030, 58018150, 197727023, 676290905, 2320721255] "" "Class ", 4362, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 0]]} "Class ", 4363, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 5, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 1, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 2, 3, 5, 4], [1, 1, 0, 0]]} "Class ", 4364, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 5, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 5, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 4, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1221, 3939, 12886, 42648, 142544, 480459, 1631287, 5574073, 19153815, 66146259, 229452587, 799140681, 2793373937] "" "Class ", 4365, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 4366, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 5, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 2, 3, 5, 4], [0, 1, 1, 0]]} "Class ", 4367, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 5, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 2, 3, 5, 4], [1, 1, 1, 0]]} "Class ", 4368, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]} "Class ", 4369, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]} "Class ", 4370, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]} "Class ", 4371, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 5, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 2, 3, 5, 4], [1, 1, 0, 1]]} "Class ", 4372, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 5, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 3, 2, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 5, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 3, 2, 1], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 4, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1221, 3939, 12886, 42648, 142544, 480459, 1631287, 5574073, 19153815, 66146259, 229452587, 799140681, 2793373937] "" "Class ", 4373, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 5, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 3, 2, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 5, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 3, 2, 1], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 4374, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 5, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 3, 2, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 2, 3, 5, 4], [0, 1, 1, 1]]} "Class ", 4375, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 3, 5, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 3, 2, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3, 4, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 2, 3, 5, 4], [1, 1, 1, 1]]} "Class ", 4376, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3, 5, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3, 5, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 0]]} "Class ", 4377, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3, 5, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 3, 5, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 3, 1, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3, 5, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 1, 3, 5, 4], [1, 1, 0, 0]]} "Class ", 4378, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3, 5, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 3, 5, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3, 5, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 1, 3, 5, 4], [0, 1, 1, 0]]} "Class ", 4379, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3, 5, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 3, 5, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 3, 1, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3, 5, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 1, 3, 5, 4], [1, 1, 1, 0]]} "Class ", 4380, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3, 5, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 3, 1, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3, 5, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]} "Class ", 4381, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3, 5, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 3, 5, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 3, 1, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 3, 1, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3, 5, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 1, 3, 5, 4], [1, 1, 0, 1]]} "Class ", 4382, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3, 5, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 3, 5, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 3, 1, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3, 5, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 1, 3, 5, 4], [0, 1, 1, 1]]} "Class ", 4383, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3, 5, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 3, 5, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 3, 1, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 3, 1, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3, 5, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 1, 3, 5, 4], [1, 1, 1, 1]]} "Class ", 4384, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 2, 5, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 2, 5, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4385, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4386, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 2, 5, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 4, 1, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 2, 5, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 4, 1, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4387, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 2, 5, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 4, 1, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 2, 5, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 4, 1, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4388, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 2, 5, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 2, 5, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4389, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4390, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 2, 5, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 4, 1, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 2, 5, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 4, 1, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4391, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 2, 5, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 4, 1, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 2, 5, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 4, 1, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4392, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2, 5, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 4, 1, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2, 5, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 4, 1, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4393, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2, 5, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 4, 1, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2, 5, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 4, 1, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4394, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2, 5, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 4, 1, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2, 5, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 4, 1, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4395, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2, 5, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 4, 1, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2, 5, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 4, 1, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4396, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2, 5, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 4, 1, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 2, 1, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2, 5, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 4, 1, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 2, 1, 3], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4397, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2, 5, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 4, 1, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 2, 1, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2, 5, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 4, 1, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 2, 1, 3], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4398, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2, 5, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 4, 1, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 2, 1, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2, 5, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 4, 1, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 2, 1, 3], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4399, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2, 5, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 4, 1, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 2, 1, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2, 5, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 4, 1, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 2, 1, 3], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4400, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1, 5, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1, 5, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4401, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4402, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1, 5, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 5, 1, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1, 5, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 5, 1, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4403, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1, 5, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 5, 1, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1, 5, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 5, 1, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4404, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1, 5, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1, 5, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4405, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4406, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1, 5, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 5, 1, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1, 5, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 5, 1, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4407, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1, 5, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 5, 1, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1, 5, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 5, 1, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4408, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1, 5, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 5, 1, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1, 5, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 5, 1, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4409, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1, 5, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1, 5, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4410, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1, 5, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 5, 1, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1, 5, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 5, 1, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4411, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1, 5, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 5, 1, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1, 5, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 5, 1, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4412, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1, 5, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 5, 1, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1, 5, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 5, 1, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4413, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1, 5, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1, 5, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4414, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1, 5, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 5, 1, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1, 5, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 5, 1, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4415, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1, 5, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 5, 1, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1, 5, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 5, 1, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4416, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 3, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 3, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 3, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 3, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4157, 13863, 46827, 159886, 550943, 1913526, 6691891, 23544320, 83280751, 295986327, 1056461081, 3785365874] "" "Class ", 4417, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 3, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 3, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [ [2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1220, 3929, 12822, 42309, 140922, 473169, 1599864, 5442561, 18615176, 63975857, 220816906, 765121477, 2660426630] "" "Class ", 4418, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 3, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 5, 2, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 3, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 5, 2, 1], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1158, 3615, 11393, 36209, 115940, 373709, 1211740, 3949969, 12937612, 42558745, 140547051, 465799527, 1548766044] "" "Class ", 4419, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 3, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 3, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 5, 2, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 3, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 3, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 5, 2, 1], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [ [2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 4420, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 3, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 3, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 5, 2, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 2, 5, 3, 4], [0, 0, 1, 0]]} "Class ", 4421, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 3, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 3, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 5, 2, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 2, 5, 3, 4], [1, 0, 1, 0]]} "Class ", 4422, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 3, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 3, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 5, 2, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 3, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 3, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 5, 2, 1], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1158, 3615, 11393, 36209, 115940, 373709, 1211740, 3949969, 12937612, 42558745, 140547051, 465799527, 1548766044] "" "Class ", 4423, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 3, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 3, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 5, 2, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 3, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 3, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 5, 2, 1], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [ [2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 4424, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 3, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 5, 2, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 2, 5, 3, 4], [0, 0, 0, 1]]} "Class ", 4425, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 3, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 5, 2, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 2, 5, 3, 4], [1, 0, 0, 1]]} "Class ", 4426, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 3, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 5, 2, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 2, 5, 3, 4], [0, 1, 0, 1]]} "Class ", 4427, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 3, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 5, 2, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 2, 5, 3, 4], [1, 1, 0, 1]]} "Class ", 4428, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 3, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 3, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 5, 2, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 2, 5, 3, 4], [0, 0, 1, 1]]} "Class ", 4429, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 3, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 3, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 5, 2, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 2, 5, 3, 4], [1, 0, 1, 1]]} "Class ", 4430, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 3, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 5, 2, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 2, 5, 3, 4], [0, 1, 1, 1]]} "Class ", 4431, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 3, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 3, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 5, 2, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 1, 4, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 2, 5, 3, 4], [1, 1, 1, 1]]} "Class ", 4432, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 1, 5, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 5, 1, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 1, 5, 4], [0, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 3, 1, 5, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 5, 1, 2], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 3, 1, 5, 4], [0, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2, 5], {3, 5}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4433, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 1, 5, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 5, 3, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 1, 3, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 5, 1, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 1, 5, 4], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 3, 1, 5, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 5, 3, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 1, 3, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 5, 1, 2], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 3, 1, 5, 4], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2, 5], {3, 5}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4434, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 1, 5, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 5, 3, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 1, 3, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 5, 1, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 1, 5, 4], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 3, 1, 5, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 5, 3, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 1, 3, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 5, 1, 2], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 3, 1, 5, 4], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2, 5], {3, 5}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4435, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 1, 5, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 5, 3, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 1, 3, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 5, 1, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 1, 5, 4], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 3, 1, 5, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 5, 3, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 1, 3, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 5, 1, 2], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 3, 1, 5, 4], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2, 5], {3, 5}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4436, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 1, 5, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 5, 1, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 1, 5, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]} "Class ", 4437, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 1, 5, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 5, 3, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 1, 3, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 5, 1, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 1, 5, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 1, 5, 3, 4], [1, 1, 0, 1]]} "Class ", 4438, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 1, 5, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 5, 3, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 1, 3, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 5, 1, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 1, 5, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 1, 5, 3, 4], [0, 1, 1, 1]]} "Class ", 4439, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 1, 5, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 5, 3, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 1, 3, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 5, 1, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 1, 5, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 1, 5, 3, 4], [1, 1, 1, 1]]} "Class ", 4440, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 2, 3, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 4, 3, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 4, 1, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 2, 3, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 4, 3, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 3, 4, 1, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4157, 13863, 46827, 159886, 550943, 1913526, 6691891, 23544320, 83280751, 295986327, 1056461081, 3785365874] "" "Class ", 4441, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 2, 3, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 4, 3, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 4, 1, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 2, 3, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 4, 3, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 3, 4, 1, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 4442, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 1, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 2, 3, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 4, 3, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 2, 5, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 4, 1, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 2, 3, 4], [0, 1, 0, 0]]} "Class ", 4443, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 1, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 2, 3, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 4, 3, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 2, 5, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 4, 1, 5], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 1, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 2, 3, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 4, 3, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 2, 5, 1], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 3, 4, 1, 5], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 4444, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 1, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 2, 3, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 4, 3, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 2, 5, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 4, 1, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 2, 3, 4], [0, 0, 1, 0]]} "Class ", 4445, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 1, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 2, 3, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 4, 3, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 2, 5, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 4, 1, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 5, 2, 3, 4], [1, 0, 1, 0]]} "Class ", 4446, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 1, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 2, 3, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 4, 3, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 2, 5, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 4, 1, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 2, 3, 4], [0, 1, 1, 0]]} "Class ", 4447, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 1, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 2, 3, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 4, 3, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 2, 5, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 4, 1, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 5, 2, 3, 4], [1, 1, 1, 0]]} "Class ", 4448, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 1, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 2, 3, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 4, 3, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 2, 5, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 4, 1, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 2, 3, 4], [0, 0, 0, 1]]} "Class ", 4449, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 1, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 2, 3, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 4, 3, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 2, 5, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 4, 1, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 5, 2, 3, 4], [1, 0, 0, 1]]} "Class ", 4450, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 1, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 2, 3, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 4, 3, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 2, 5, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 4, 1, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 2, 3, 4], [0, 1, 0, 1]]} "Class ", 4451, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 1, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 2, 3, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 4, 3, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 2, 5, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 4, 1, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 5, 2, 3, 4], [1, 1, 0, 1]]} "Class ", 4452, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 1, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 2, 3, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 4, 3, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 2, 5, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 4, 1, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 2, 3, 4], [0, 0, 1, 1]]} "Class ", 4453, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 1, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 2, 3, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 4, 3, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 2, 5, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 4, 1, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 5, 2, 3, 4], [1, 0, 1, 1]]} "Class ", 4454, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 1, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 2, 3, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 4, 3, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 2, 5, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 4, 1, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 2, 3, 4], [0, 1, 1, 1]]} "Class ", 4455, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 1, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 2, 3, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 4, 3, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 2, 5, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 4, 1, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 5, 2, 3, 4], [1, 1, 1, 1]]} "Class ", 4456, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [ [1, 2, 3, 4, 5], {1}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1210, 3865, 12482, 40677, 133572, 441468, 1467296, 4900760, 16439370, 55357305, 187050302, 633998079, 2154950454] "" "Class ", 4457, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1210, 3865, 12482, 40677, 133572, 441468, 1467296, 4900760, 16439370, 55357305, 187050302, 633998079, 2154950454] "" "Class ", 4458, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 5, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 2, 3, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 4, 3, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 4, 5, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 2, 3, 4], [0, 1, 0, 0]]} "Class ", 4459, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 5, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 4, 3, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 4, 5, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]} "Class ", 4460, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 5, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 2, 3, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 4, 3, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 2, 1, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 4, 5, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 2, 3, 4], [0, 0, 1, 0]]} "Class ", 4461, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 5, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 2, 3, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 4, 3, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 2, 1, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 4, 5, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 2, 3, 4], [1, 0, 1, 0]]} "Class ", 4462, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 5, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 2, 3, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 4, 3, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 2, 1, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 4, 5, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 2, 3, 4], [0, 1, 1, 0]]} "Class ", 4463, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 5, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 2, 3, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 4, 3, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 2, 1, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 4, 5, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 2, 3, 4], [1, 1, 1, 0]]} "Class ", 4464, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 5, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 2, 1, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 4, 5, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]} "Class ", 4465, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 5, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 2, 1, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 4, 5, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]} "Class ", 4466, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 5, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 2, 3, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 4, 3, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 2, 1, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 4, 5, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 2, 3, 4], [0, 1, 0, 1]]} "Class ", 4467, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 5, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 2, 1, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 4, 5, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]} "Class ", 4468, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 5, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 2, 3, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 4, 3, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 2, 1, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 4, 5, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 2, 3, 4], [0, 0, 1, 1]]} "Class ", 4469, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 5, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 2, 3, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 4, 3, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 2, 1, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 4, 5, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 2, 3, 4], [1, 0, 1, 1]]} "Class ", 4470, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 5, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 2, 3, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 4, 3, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 2, 1, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 4, 5, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 2, 3, 4], [0, 1, 1, 1]]} "Class ", 4471, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 5, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 4, 5, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]} "Class ", 4472, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 5, 1, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 1, 3, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 5, 3, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 1, 5, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 5, 1, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[2, 5, 1, 3, 4], [0, 0, 1, 0]]} "Class ", 4473, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 5, 1, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 1, 3, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 5, 3, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 1, 5, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 5, 1, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[2, 5, 1, 3, 4], [1, 0, 1, 0]]} "Class ", 4474, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 5, 1, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 1, 3, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 5, 3, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 1, 5, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 5, 1, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 5, 1, 3, 4], [0, 1, 1, 0]]} "Class ", 4475, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 5, 1, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 1, 3, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 5, 3, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 1, 5, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 5, 1, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 5, 1, 3, 4], [1, 1, 1, 0]]} "Class ", 4476, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 5, 1, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 1, 3, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 5, 3, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 1, 5, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 5, 1, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[2, 5, 1, 3, 4], [0, 0, 1, 1]]} "Class ", 4477, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 5, 1, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 1, 3, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 5, 3, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 1, 5, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 5, 1, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[2, 5, 1, 3, 4], [1, 0, 1, 1]]} "Class ", 4478, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 5, 1, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 1, 3, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 5, 3, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 1, 5, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 5, 1, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 5, 1, 3, 4], [0, 1, 1, 1]]} "Class ", 4479, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 5, 1, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 1, 3, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 5, 3, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 1, 5, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 5, 1, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 5, 1, 3, 4], [1, 1, 1, 1]]} "Class ", 4480, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 5, 4, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 1, 3, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 5, 3, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 1, 2, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 5, 4, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 2, 1, 3, 4], [0, 0, 1, 0]]} "Class ", 4481, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 5, 4, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 1, 3, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 5, 3, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 1, 2, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 5, 4, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 2, 1, 3, 4], [1, 0, 1, 0]]} "Class ", 4482, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 5, 4, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 1, 3, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 5, 3, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 1, 2, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 5, 4, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 2, 1, 3, 4], [0, 1, 1, 0]]} "Class ", 4483, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 5, 4, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 1, 3, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 5, 3, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 1, 2, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 5, 4, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 2, 1, 3, 4], [1, 1, 1, 0]]} "Class ", 4484, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 5, 4, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 1, 3, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 5, 3, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 1, 2, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 5, 4, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 2, 1, 3, 4], [0, 0, 1, 1]]} "Class ", 4485, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 5, 4, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 1, 3, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 5, 3, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 1, 2, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 5, 4, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 2, 1, 3, 4], [1, 0, 1, 1]]} "Class ", 4486, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 5, 4, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 1, 3, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 5, 3, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 1, 2, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 5, 4, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 2, 1, 3, 4], [0, 1, 1, 1]]} "Class ", 4487, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 5, 4, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 1, 3, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 5, 3, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 3, 1, 2, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 5, 4, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 2, 1, 3, 4], [1, 1, 1, 1]]} "Class ", 4488, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 1, 3, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 5, 2, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 1, 4, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 5, 3, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 1, 3, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 3, 5, 2, 4], [0, 0, 0, 1]]} "Class ", 4489, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 1, 3, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 5, 2, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 1, 4, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 5, 3, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 1, 3, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 3, 5, 2, 4], [1, 0, 0, 1]]} "Class ", 4490, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 1, 3, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 5, 2, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 1, 4, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 5, 3, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 1, 3, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 3, 5, 2, 4], [0, 1, 0, 1]]} "Class ", 4491, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 1, 3, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 5, 2, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 1, 4, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 5, 3, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 1, 3, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 3, 5, 2, 4], [1, 1, 0, 1]]} "Class ", 4492, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 1, 3, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 5, 2, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 1, 4, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 5, 3, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 1, 3, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 3, 5, 2, 4], [0, 0, 1, 1]]} "Class ", 4493, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 1, 3, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 5, 2, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 1, 4, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 5, 3, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 1, 3, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 3, 5, 2, 4], [1, 0, 1, 1]]} "Class ", 4494, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 1, 3, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 5, 2, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 1, 4, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 5, 3, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 1, 3, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 3, 5, 2, 4], [0, 1, 1, 1]]} "Class ", 4495, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 1, 3, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 5, 2, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 1, 4, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 5, 3, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 1, 3, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 3, 5, 2, 4], [1, 1, 1, 1]]} "Class ", 4496, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 1, 5, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 5, 2, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 1, 4, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 5, 1, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 1, 5, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 1, 5, 2, 4], [0, 1, 0, 1]]} "Class ", 4497, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 1, 5, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 5, 2, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 1, 4, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 5, 1, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 1, 5, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[3, 1, 5, 2, 4], [1, 1, 0, 1]]} "Class ", 4498, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 1, 5, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 5, 2, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 1, 4, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 5, 1, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 1, 5, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 1, 5, 2, 4], [0, 1, 1, 1]]} "Class ", 4499, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 1, 5, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 5, 2, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 1, 4, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 5, 1, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 1, 5, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[3, 1, 5, 2, 4], [1, 1, 1, 1]]} "Class ", 4500, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 3, 1, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 3, 2, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 3, 4, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 3, 5, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 3, 1, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 3, 2, 4], [0, 0, 0, 1]]} "Class ", 4501, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 3, 1, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 3, 2, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 3, 4, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 3, 5, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 3, 1, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 5, 3, 2, 4], [1, 0, 0, 1]]} "Class ", 4502, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 3, 1, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 3, 2, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 3, 4, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 3, 5, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 3, 1, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 3, 2, 4], [0, 1, 0, 1]]} "Class ", 4503, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 3, 1, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 3, 2, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 3, 4, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 3, 5, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 3, 1, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 5, 3, 2, 4], [1, 1, 0, 1]]} "Class ", 4504, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 3, 1, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 3, 2, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 3, 4, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 3, 5, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 3, 1, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 3, 2, 4], [0, 0, 1, 1]]} "Class ", 4505, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 3, 1, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 3, 2, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 3, 4, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 3, 5, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 3, 1, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 5, 3, 2, 4], [1, 0, 1, 1]]} "Class ", 4506, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 3, 1, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 3, 2, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 3, 4, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 3, 5, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 3, 1, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 3, 2, 4], [0, 1, 1, 1]]} "Class ", 4507, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 3, 1, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 3, 2, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 3, 4, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 3, 5, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 3, 1, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 5, 3, 2, 4], [1, 1, 1, 1]]} "Class ", 4508, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 3, 5, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 3, 2, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 3, 4, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 3, 1, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 3, 5, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 3, 2, 4], [0, 0, 0, 1]]} "Class ", 4509, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 3, 5, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 3, 2, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 3, 4, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 3, 1, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 3, 5, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 3, 2, 4], [1, 0, 0, 1]]} "Class ", 4510, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 3, 5, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 3, 2, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 3, 4, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 3, 1, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 3, 5, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 3, 2, 4], [0, 1, 0, 1]]} "Class ", 4511, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 3, 5, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 3, 2, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 3, 4, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 3, 1, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 3, 5, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 3, 2, 4], [1, 1, 0, 1]]} "Class ", 4512, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 3, 5, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 3, 2, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 3, 4, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 3, 1, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 3, 5, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 3, 2, 4], [0, 0, 1, 1]]} "Class ", 4513, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 3, 5, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 3, 2, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 3, 4, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 3, 1, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 3, 5, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 3, 2, 4], [1, 0, 1, 1]]} "Class ", 4514, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 3, 5, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 3, 2, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 3, 4, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 3, 1, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 3, 5, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 3, 2, 4], [0, 1, 1, 1]]} "Class ", 4515, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 3, 5, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 3, 2, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 3, 4, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 3, 1, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 3, 5, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 3, 2, 4], [1, 1, 1, 1]]} "Class ", 4516, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 5, 1, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 5, 4, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 1, 5, 3], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 5, 1, 3], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 1]]} "Class ", 4517, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 5, 1, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 1, 2, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 5, 4, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 1, 5, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 5, 1, 3], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[3, 5, 1, 2, 4], [1, 0, 0, 1]]} "Class ", 4518, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 5, 1, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 1, 2, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 5, 4, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 1, 5, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 5, 1, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 5, 1, 2, 4], [0, 1, 0, 1]]} "Class ", 4519, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 5, 1, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 1, 2, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 5, 4, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 1, 5, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 5, 1, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[3, 5, 1, 2, 4], [1, 1, 0, 1]]} "Class ", 4520, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 5, 1, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 1, 2, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 5, 4, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 1, 5, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 5, 1, 3], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[3, 5, 1, 2, 4], [0, 0, 1, 1]]} "Class ", 4521, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 5, 1, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 1, 2, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 5, 4, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 1, 5, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 5, 1, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[3, 5, 1, 2, 4], [1, 0, 1, 1]]} "Class ", 4522, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 5, 1, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 1, 2, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 5, 4, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 1, 5, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 5, 1, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 5, 1, 2, 4], [0, 1, 1, 1]]} "Class ", 4523, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 5, 1, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 1, 2, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 5, 4, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 1, 5, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 5, 1, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[3, 5, 1, 2, 4], [1, 1, 1, 1]]} "Class ", 4524, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 5, 3, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 5, 4, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 1, 3, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 5, 3, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 1]]} "Class ", 4525, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 5, 3, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 5, 4, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 1, 3, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 5, 3, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]} "Class ", 4526, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 5, 3, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 1, 2, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 5, 4, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 1, 3, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 5, 3, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 3, 1, 2, 4], [0, 1, 0, 1]]} "Class ", 4527, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 5, 3, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 1, 2, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 5, 4, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 1, 3, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 5, 3, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 3, 1, 2, 4], [1, 1, 0, 1]]} "Class ", 4528, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 5, 3, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 1, 2, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 5, 4, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 1, 3, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 5, 3, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 3, 1, 2, 4], [0, 0, 1, 1]]} "Class ", 4529, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 5, 3, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 1, 2, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 5, 4, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 1, 3, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 5, 3, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 3, 1, 2, 4], [1, 0, 1, 1]]} "Class ", 4530, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 5, 3, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 1, 2, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 5, 4, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 1, 3, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 5, 3, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 3, 1, 2, 4], [0, 1, 1, 1]]} "Class ", 4531, " is:" {{[[1, 3, 2], [0, 1]], [[2, 4, 5, 3, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 1, 2, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 5, 4, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 2, 1, 3, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 4, 5, 3, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 3, 1, 2, 4], [1, 1, 1, 1]]} "Class ", 4532, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 1, 3, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 5, 1, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 1, 5, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 5, 3, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 1, 3, 4], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[2, 3, 5, 1, 4], [0, 0, 0, 1]]} "Class ", 4533, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 1, 3, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 5, 1, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 1, 5, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 5, 3, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 1, 3, 4], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[2, 3, 5, 1, 4], [1, 0, 0, 1]]} "Class ", 4534, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 1, 3, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 5, 1, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 1, 5, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 5, 3, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 1, 3, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 3, 5, 1, 4], [0, 1, 0, 1]]} "Class ", 4535, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 1, 3, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 5, 1, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 1, 5, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 5, 3, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 1, 3, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 3, 5, 1, 4], [1, 1, 0, 1]]} "Class ", 4536, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 1, 3, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 5, 1, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 1, 5, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 5, 3, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 1, 3, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[2, 3, 5, 1, 4], [0, 0, 1, 1]]} "Class ", 4537, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 1, 3, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 5, 1, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 1, 5, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 5, 3, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 1, 3, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[2, 3, 5, 1, 4], [1, 0, 1, 1]]} "Class ", 4538, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 1, 3, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 5, 1, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 1, 5, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 5, 3, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 1, 3, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 3, 5, 1, 4], [0, 1, 1, 1]]} "Class ", 4539, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 1, 3, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 5, 1, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 1, 5, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 5, 3, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 1, 3, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 3, 5, 1, 4], [1, 1, 1, 1]]} "Class ", 4540, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 1, 4, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 5, 1, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 1, 5, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 5, 2, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 1, 4, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 2, 5, 1, 4], [0, 1, 0, 1]]} "Class ", 4541, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 1, 4, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 5, 1, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 1, 5, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 5, 2, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 1, 4, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[3, 2, 5, 1, 4], [1, 1, 0, 1]]} "Class ", 4542, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 1, 4, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 5, 1, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 1, 5, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 5, 2, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 1, 4, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 2, 5, 1, 4], [0, 1, 1, 1]]} "Class ", 4543, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 1, 4, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 5, 1, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 1, 5, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 5, 2, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 1, 4, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[3, 2, 5, 1, 4], [1, 1, 1, 1]]} "Class ", 4544, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 3, 1, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 3, 1, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 3, 5, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 3, 5, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 3, 1, 4], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[2, 5, 3, 1, 4], [0, 0, 0, 1]]} "Class ", 4545, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 3, 1, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 3, 1, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 3, 5, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 3, 5, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 3, 1, 4], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[2, 5, 3, 1, 4], [1, 0, 0, 1]]} "Class ", 4546, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 3, 1, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 3, 1, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 3, 5, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 3, 5, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 3, 1, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 5, 3, 1, 4], [0, 1, 0, 1]]} "Class ", 4547, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 3, 1, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 3, 1, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 3, 5, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 3, 5, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 3, 1, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 5, 3, 1, 4], [1, 1, 0, 1]]} "Class ", 4548, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 3, 1, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 3, 1, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 3, 5, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 3, 5, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 3, 1, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[2, 5, 3, 1, 4], [0, 0, 1, 1]]} "Class ", 4549, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 3, 1, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 3, 1, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 3, 5, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 3, 5, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 3, 1, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[2, 5, 3, 1, 4], [1, 0, 1, 1]]} "Class ", 4550, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 3, 1, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 3, 1, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 3, 5, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 3, 5, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 3, 1, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 5, 3, 1, 4], [0, 1, 1, 1]]} "Class ", 4551, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 3, 1, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 3, 1, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 3, 5, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 3, 5, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 3, 1, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 5, 3, 1, 4], [1, 1, 1, 1]]} "Class ", 4552, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 3, 4, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 3, 1, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 3, 5, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 3, 2, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 3, 4, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 2, 3, 1, 4], [0, 0, 0, 1]]} "Class ", 4553, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 3, 4, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 3, 5, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 3, 2, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 3, 4, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 1]]} "Class ", 4554, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 3, 4, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 3, 1, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 3, 5, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 3, 2, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 3, 4, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 2, 3, 1, 4], [0, 1, 0, 1]]} "Class ", 4555, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 3, 4, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 3, 1, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 3, 5, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 3, 2, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 3, 4, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 2, 3, 1, 4], [1, 1, 0, 1]]} "Class ", 4556, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 3, 4, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 3, 1, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 3, 5, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 3, 2, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 3, 4, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 2, 3, 1, 4], [0, 0, 1, 1]]} "Class ", 4557, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 3, 4, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 3, 1, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 3, 5, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 3, 2, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 3, 4, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 2, 3, 1, 4], [1, 0, 1, 1]]} "Class ", 4558, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 3, 4, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 3, 1, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 3, 5, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 3, 2, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 3, 4, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 2, 3, 1, 4], [0, 1, 1, 1]]} "Class ", 4559, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 3, 4, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 3, 1, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 3, 5, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 3, 2, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 3, 4, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 2, 3, 1, 4], [1, 1, 1, 1]]} "Class ", 4560, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 4, 1, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 4, 5, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 2, 5, 3], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 4, 1, 3], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 1]]} "Class ", 4561, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 4, 1, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 2, 1, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 4, 5, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 2, 5, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 4, 1, 3], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[3, 5, 2, 1, 4], [1, 0, 0, 1]]} "Class ", 4562, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 4, 1, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 2, 1, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 4, 5, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 2, 5, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 4, 1, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 5, 2, 1, 4], [0, 1, 0, 1]]} "Class ", 4563, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 4, 1, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 2, 1, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 4, 5, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 2, 5, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 4, 1, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[3, 5, 2, 1, 4], [1, 1, 0, 1]]} "Class ", 4564, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 4, 1, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 2, 1, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 4, 5, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 2, 5, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 4, 1, 3], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[3, 5, 2, 1, 4], [0, 0, 1, 1]]} "Class ", 4565, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 4, 1, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 2, 1, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 4, 5, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 2, 5, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 4, 1, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[3, 5, 2, 1, 4], [1, 0, 1, 1]]} "Class ", 4566, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 4, 1, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 2, 1, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 4, 5, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 2, 5, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 4, 1, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 5, 2, 1, 4], [0, 1, 1, 1]]} "Class ", 4567, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 4, 1, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 2, 1, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 4, 5, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 2, 5, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 4, 1, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[3, 5, 2, 1, 4], [1, 1, 1, 1]]} "Class ", 4568, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 4, 3, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 2, 3, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 4, 3, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]} "Class ", 4569, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 4, 3, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 2, 3, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 4, 3, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]} "Class ", 4570, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 4, 3, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 2, 1, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 4, 5, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 2, 3, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 4, 3, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 3, 2, 1, 4], [0, 1, 0, 1]]} "Class ", 4571, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 4, 3, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 2, 1, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 4, 5, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 2, 3, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 4, 3, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 3, 2, 1, 4], [1, 1, 0, 1]]} "Class ", 4572, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 4, 3, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 2, 1, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 4, 5, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 2, 3, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 4, 3, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 3, 2, 1, 4], [0, 0, 1, 1]]} "Class ", 4573, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 4, 3, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 2, 1, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 4, 5, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 2, 3, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 4, 3, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 3, 2, 1, 4], [1, 0, 1, 1]]} "Class ", 4574, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 4, 3, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 2, 1, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 4, 5, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 2, 3, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 4, 3, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 3, 2, 1, 4], [0, 1, 1, 1]]} "Class ", 4575, " is:" {{[[1, 3, 2], [0, 1]], [[2, 5, 4, 3, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 2, 1, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 4, 5, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[4, 1, 2, 3, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 5, 4, 3, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 3, 2, 1, 4], [1, 1, 1, 1]]} "Class ", 4576, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 2, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 4, 2, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 2, 4, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 1, 2, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 4, 2, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 1, 2, 4, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 1, 0, 0]}], [[3, 1, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 3, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 401, 1310, 4368, 14806, 50868, 176738, 619932, 2192288, 7807625, 27978530, 100809146, 364990184, 1327233335, 4845181810] "" "Class ", 4577, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 2, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 4, 2, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 2, 4, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 1, 2, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 4, 2, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 1, 2, 4, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4158, 13873, 46893, 160247, 552723, 1921756, 6728347, 23701026, 83939765, 298712615, 1067598164, 3830414563] "" "Class ", 4578, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 2, 4, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 4, 2, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 2, 4, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 0]]} "Class ", 4579, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 2, 4, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 4, 5, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 2, 1, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 4, 2, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 2, 4, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 2, 4, 5, 3], [1, 1, 0, 0]]} "Class ", 4580, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 2, 4, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 4, 5, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 2, 1, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 4, 2, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 2, 4, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 2, 4, 5, 3], [0, 0, 1, 0]]} "Class ", 4581, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 2, 4, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 4, 5, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 2, 1, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 4, 2, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 2, 4, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 2, 4, 5, 3], [1, 0, 1, 0]]} "Class ", 4582, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 2, 4, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 4, 5, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 2, 1, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 4, 2, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 2, 4, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 2, 4, 5, 3], [0, 1, 1, 0]]} "Class ", 4583, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 2, 4, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 4, 5, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 2, 1, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 4, 2, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 2, 4, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 2, 4, 5, 3], [1, 1, 1, 0]]} "Class ", 4584, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 2, 4, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 2, 4, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]} "Class ", 4585, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 2, 4, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 2, 4, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]} "Class ", 4586, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 2, 4, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 2, 4, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]} "Class ", 4587, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 2, 4, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 2, 4, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]} "Class ", 4588, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 2, 4, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 4, 5, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 2, 1, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 4, 2, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 2, 4, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 2, 4, 5, 3], [0, 0, 1, 1]]} "Class ", 4589, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 2, 4, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 4, 5, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 2, 1, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 4, 2, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 2, 4, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 2, 4, 5, 3], [1, 0, 1, 1]]} "Class ", 4590, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 2, 4, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 4, 5, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 2, 1, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 4, 2, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 2, 4, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 2, 4, 5, 3], [0, 1, 1, 1]]} "Class ", 4591, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 2, 4, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 4, 5, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 2, 1, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 4, 2, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 2, 4, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 2, 4, 5, 3], [1, 1, 1, 1]]} "Class ", 4592, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 2, 5, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 4, 1, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 2, 5, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 0]]} "Class ", 4593, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 2, 5, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 4, 5, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 2, 1, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 4, 1, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 2, 5, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 1, 4, 5, 3], [1, 1, 0, 0]]} "Class ", 4594, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 2, 5, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 4, 5, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 4, 1, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 2, 5, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 1, 4, 5, 3], [0, 1, 1, 0]]} "Class ", 4595, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 2, 5, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 4, 5, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 2, 1, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 4, 1, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 2, 5, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 1, 4, 5, 3], [1, 1, 1, 0]]} "Class ", 4596, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 2, 5, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 4, 1, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 2, 5, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]} "Class ", 4597, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 2, 5, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 4, 5, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 2, 1, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 4, 1, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 2, 5, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 1, 4, 5, 3], [1, 1, 0, 1]]} "Class ", 4598, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 2, 5, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 4, 5, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 4, 1, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 2, 5, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 1, 4, 5, 3], [0, 1, 1, 1]]} "Class ", 4599, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 2, 5, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 4, 5, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 2, 1, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 4, 1, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 2, 5, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 1, 4, 5, 3], [1, 1, 1, 1]]} "Class ", 4600, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 4, 2, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 2, 5, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 4, 1, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 2, 4, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 4, 2, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 4, 2, 5, 3], [0, 0, 1, 0]]} "Class ", 4601, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 4, 2, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 2, 5, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 4, 1, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 2, 4, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 4, 2, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 4, 2, 5, 3], [1, 0, 1, 0]]} "Class ", 4602, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 4, 2, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 2, 5, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 4, 1, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 2, 4, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 4, 2, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 4, 2, 5, 3], [0, 1, 1, 0]]} "Class ", 4603, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 4, 2, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 2, 5, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 4, 1, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 2, 4, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 4, 2, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 4, 2, 5, 3], [1, 1, 1, 0]]} "Class ", 4604, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 4, 2, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 2, 5, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 4, 1, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 2, 4, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 4, 2, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 4, 2, 5, 3], [0, 0, 1, 1]]} "Class ", 4605, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 4, 2, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 2, 5, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 4, 1, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 2, 4, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 4, 2, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 4, 2, 5, 3], [1, 0, 1, 1]]} "Class ", 4606, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 4, 2, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 2, 5, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 4, 1, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 2, 4, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 4, 2, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 4, 2, 5, 3], [0, 1, 1, 1]]} "Class ", 4607, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 4, 2, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 2, 5, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 4, 1, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 2, 4, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 4, 2, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 4, 2, 5, 3], [1, 1, 1, 1]]} "Class ", 4608, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 4, 5, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 2, 5, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 4, 1, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 2, 1, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 4, 5, 2], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[4, 1, 2, 5, 3], [0, 0, 1, 0]]} "Class ", 4609, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 4, 5, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 2, 5, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 4, 1, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 2, 1, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 4, 5, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[4, 1, 2, 5, 3], [1, 0, 1, 0]]} "Class ", 4610, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 4, 5, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 2, 5, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 4, 1, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 2, 1, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 4, 5, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 1, 2, 5, 3], [0, 1, 1, 0]]} "Class ", 4611, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 4, 5, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 2, 5, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 4, 1, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 2, 1, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 4, 5, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 1, 2, 5, 3], [1, 1, 1, 0]]} "Class ", 4612, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 4, 5, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 2, 5, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 4, 1, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 2, 1, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 4, 5, 2], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[4, 1, 2, 5, 3], [0, 0, 1, 1]]} "Class ", 4613, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 4, 5, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 2, 5, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 4, 1, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 2, 1, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 4, 5, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[4, 1, 2, 5, 3], [1, 0, 1, 1]]} "Class ", 4614, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 4, 5, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 2, 5, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 4, 1, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 2, 1, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 4, 5, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 1, 2, 5, 3], [0, 1, 1, 1]]} "Class ", 4615, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 4, 5, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 2, 5, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 4, 1, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 2, 1, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 4, 5, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 1, 2, 5, 3], [1, 1, 1, 1]]} "Class ", 4616, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 5, 2, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 1, 5, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 5, 1, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 1, 4, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 5, 2, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[2, 4, 1, 5, 3], [0, 0, 1, 0]]} "Class ", 4617, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 5, 2, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 1, 5, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 5, 1, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 1, 4, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 5, 2, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[2, 4, 1, 5, 3], [1, 0, 1, 0]]} "Class ", 4618, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 5, 2, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 1, 5, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 5, 1, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 1, 4, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 5, 2, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 4, 1, 5, 3], [0, 1, 1, 0]]} "Class ", 4619, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 5, 2, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 1, 5, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 5, 1, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 1, 4, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 5, 2, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 4, 1, 5, 3], [1, 1, 1, 0]]} "Class ", 4620, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 5, 2, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 1, 5, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 5, 1, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 1, 4, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 5, 2, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[2, 4, 1, 5, 3], [0, 0, 1, 1]]} "Class ", 4621, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 5, 2, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 1, 5, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 5, 1, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 1, 4, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 5, 2, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[2, 4, 1, 5, 3], [1, 0, 1, 1]]} "Class ", 4622, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 5, 2, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 1, 5, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 5, 1, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 1, 4, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 5, 2, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 4, 1, 5, 3], [0, 1, 1, 1]]} "Class ", 4623, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 5, 2, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 1, 5, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 5, 1, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 1, 4, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 5, 2, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 4, 1, 5, 3], [1, 1, 1, 1]]} "Class ", 4624, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 5, 4, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 1, 5, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 5, 1, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 1, 2, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 5, 4, 2], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[4, 2, 1, 5, 3], [0, 0, 1, 0]]} "Class ", 4625, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 5, 4, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 1, 5, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 5, 1, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 1, 2, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 5, 4, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[4, 2, 1, 5, 3], [1, 0, 1, 0]]} "Class ", 4626, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 5, 4, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 1, 5, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 5, 1, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 1, 2, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 5, 4, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 2, 1, 5, 3], [0, 1, 1, 0]]} "Class ", 4627, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 5, 4, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 1, 5, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 5, 1, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 1, 2, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 5, 4, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 2, 1, 5, 3], [1, 1, 1, 0]]} "Class ", 4628, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 5, 4, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 1, 5, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 5, 1, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 1, 2, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 5, 4, 2], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[4, 2, 1, 5, 3], [0, 0, 1, 1]]} "Class ", 4629, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 5, 4, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 1, 5, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 5, 1, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 1, 2, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 5, 4, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[4, 2, 1, 5, 3], [1, 0, 1, 1]]} "Class ", 4630, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 5, 4, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 1, 5, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 5, 1, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 1, 2, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 5, 4, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 2, 1, 5, 3], [0, 1, 1, 1]]} "Class ", 4631, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 5, 4, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 1, 5, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 5, 1, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 5, 1, 2, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 5, 4, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 2, 1, 5, 3], [1, 1, 1, 1]]} "Class ", 4632, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 4, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 2, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 4, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 2, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 401, 1310, 4368, 14806, 50868, 176738, 619932, 2192288, 7807625, 27978530, 100809146, 364990184, 1327233335, 4845181810] "" "Class ", 4633, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 4, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 2, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 4, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 2, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4158, 13873, 46893, 160247, 552723, 1921756, 6728347, 23701026, 83939765, 298712615, 1067598164, 3830414563] "" "Class ", 4634, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 2, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 2, 1], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 3, 5], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 2, 5], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {1, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [ [5, 2, 1, 3, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 383, 1202, 3819, 12255, 39651, 129190, 423469, 1395425, 4619787, 15358681, 51253577, 171625635, 576499577, 1942062420] "" "Class ", 4635, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 2, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 2, 1], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [ [4, 2, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [ [4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [ [5, 2, 1, 3, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 4636, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 4, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 2, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 2, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 2, 5, 4, 3], [0, 0, 1, 0]]} "Class ", 4637, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 4, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 2, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 2, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 2, 5, 4, 3], [1, 0, 1, 0]]} "Class ", 4638, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 4, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 2, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 4, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 2, 1], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {1, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 367, 1117, 3441, 10720, 33727, 107012, 342023, 1100128, 3558535, 11568339, 37776029, 123855123, 407565811, 1345623584] "" "Class ", 4639, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 4, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 2, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 4, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 2, 1], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 356, 1044, 3057, 8948, 26192, 76674, 224465, 657137, 1923817, 5632105, 16488346, 48270655, 141315320, 413709331] "" "Class ", 4640, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 4, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 2, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 2, 5, 4, 3], [0, 0, 0, 1]]} "Class ", 4641, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 2, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]} "Class ", 4642, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 2, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 2, 1], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 3, 5], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {1, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [ [5, 2, 1, 3, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1158, 3615, 11393, 36209, 115940, 373709, 1211740, 3949969, 12937612, 42558745, 140547051, 465799527, 1548766044] "" "Class ", 4643, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 2, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 2, 1], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [ [4, 2, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [ [5, 2, 1, 3, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 4644, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 4, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 2, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 2, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 2, 5, 4, 3], [0, 0, 1, 1]]} "Class ", 4645, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 4, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 2, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 2, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 2, 5, 4, 3], [1, 0, 1, 1]]} "Class ", 4646, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 4, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 2, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 4, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 2, 1], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {1, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 367, 1117, 3441, 10720, 33727, 107012, 342023, 1100128, 3558535, 11568339, 37776029, 123855123, 407565811, 1345623584] "" "Class ", 4647, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 4, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 2, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 2, 5, 4, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 2, 1], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 356, 1044, 3057, 8948, 26192, 76674, 224465, 657137, 1923817, 5632105, 16488346, 48270655, 141315320, 413709331] "" "Class ", 4648, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [ [4, 2, 1, 3, 5], {4, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 3, 1, 2, 5], {3, 5}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 3, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4649, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 5, 4, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 1, 2, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 5, 4, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 1, 2, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [ [4, 2, 1, 3, 5], {4, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 3, 1, 2, 5], {3, 5}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 3, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4650, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 5, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 5, 4, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 1, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 1, 5, 4], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 5, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 5, 4, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 1, 2], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 2, 1, 5, 4], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4651, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 5, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 5, 4, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 1, 2, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 1, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 1, 5, 4], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 5, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 5, 4, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 1, 2, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 1, 2], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 2, 1, 5, 4], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4652, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 5, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 1, 5, 4], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 5, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 2, 1, 5, 4], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [ [4, 2, 1, 3, 5], {4, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 3, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4653, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 5, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 5, 4, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 1, 2, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 1, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 1, 5, 4], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 5, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 5, 4, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 1, 2, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 1, 2], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 2, 1, 5, 4], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [ [4, 2, 1, 3, 5], {4, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 3, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4654, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 5, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 5, 4, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 1, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 1, 5, 4], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 5, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 5, 4, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 1, 2], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 2, 1, 5, 4], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4655, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 5, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 5, 4, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 1, 2, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 1, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 1, 5, 4], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 5, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 1, 5, 4, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 5, 1, 2, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 5, 1, 2], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 2, 1, 5, 4], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 4656, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 2, 4, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 4, 2, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 2, 5, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 4, 1, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 2, 4, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 4, 2, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 2, 5, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 2, 4, 1, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}] , [[4, 3, 5, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 402, 1317, 4403, 14963, 51537, 179503, 631144, 2237199, 7986056, 28683449, 103583004, 375874395, 1369853869, 5011826841] "" "Class ", 4657, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 2, 4, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 4, 2, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 2, 5, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 4, 1, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 2, 4, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 4, 2, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 2, 5, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 2, 4, 1, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1221, 3939, 12885, 42636, 142456, 479944, 1628631, 5561411, 19096541, 65896618, 228393724, 794741412, 2775388162] "" "Class ", 4658, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 1, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 2, 4, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 4, 2, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 2, 5, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 4, 1, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 2, 4, 3], [0, 1, 0, 0]]} "Class ", 4659, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 1, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 2, 4, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 4, 2, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 2, 5, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 4, 1, 5], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 1, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 2, 4, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 4, 2, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 2, 5, 1], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 2, 4, 1, 5], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 4660, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 1, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 2, 4, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 4, 2, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 2, 5, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 4, 1, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 2, 4, 3], [0, 0, 1, 0]]} "Class ", 4661, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 1, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 2, 4, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 4, 2, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 2, 5, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 4, 1, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 5, 2, 4, 3], [1, 0, 1, 0]]} "Class ", 4662, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 1, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 2, 4, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 4, 2, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 2, 5, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 4, 1, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 2, 4, 3], [0, 1, 1, 0]]} "Class ", 4663, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 1, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 2, 4, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 4, 2, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 2, 5, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 4, 1, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 5, 2, 4, 3], [1, 1, 1, 0]]} "Class ", 4664, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 1, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 2, 4, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 4, 2, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 2, 5, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 4, 1, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 2, 4, 3], [0, 0, 0, 1]]} "Class ", 4665, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 1, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 2, 4, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 4, 2, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 2, 5, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 4, 1, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 5, 2, 4, 3], [1, 0, 0, 1]]} "Class ", 4666, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 1, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 2, 4, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 4, 2, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 2, 5, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 4, 1, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 2, 4, 3], [0, 1, 0, 1]]} "Class ", 4667, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 1, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 2, 4, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 4, 2, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 2, 5, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 4, 1, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 5, 2, 4, 3], [1, 1, 0, 1]]} "Class ", 4668, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 1, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 2, 4, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 4, 2, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 2, 5, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 4, 1, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 2, 4, 3], [0, 0, 1, 1]]} "Class ", 4669, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 1, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 2, 4, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 4, 2, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 2, 5, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 4, 1, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 5, 2, 4, 3], [1, 0, 1, 1]]} "Class ", 4670, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 1, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 2, 4, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 4, 2, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 2, 5, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 4, 1, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 2, 4, 3], [0, 1, 1, 1]]} "Class ", 4671, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 1, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 2, 4, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 4, 2, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 2, 5, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 4, 1, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 5, 2, 4, 3], [1, 1, 1, 1]]} "Class ", 4672, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 2, 4, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 4, 2, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 2, 1, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 4, 5, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 2, 4, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 4, 2, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 2, 1, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 2, 4, 5, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [ [2, 1, 3, 4, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 4, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4159, 13883, 46959, 160608, 554500, 1929947, 6764488, 23855708, 84587419, 301380544, 1078453368, 3874161462] "" "Class ", 4673, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 2, 4, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 2, 1, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 4, 5, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 2, 4, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 2, 1, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 2, 4, 5, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1211, 3875, 12548, 41040, 135370, 449791, 1504057, 5057668, 17092030, 58018150, 197727023, 676290905, 2320721255] "" "Class ", 4674, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 5, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 2, 4, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 4, 2, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 2, 1, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 4, 5, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 2, 4, 3], [0, 1, 0, 0]]} "Class ", 4675, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 5, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 2, 4, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 4, 2, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 2, 1, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 4, 5, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 2, 4, 3], [1, 1, 0, 0]]} "Class ", 4676, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 5, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 2, 4, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 4, 2, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 2, 1, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 4, 5, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 2, 4, 3], [0, 0, 1, 0]]} "Class ", 4677, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 5, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 2, 4, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 4, 2, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 2, 1, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 4, 5, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 2, 4, 3], [1, 0, 1, 0]]} "Class ", 4678, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 5, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 2, 4, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 4, 2, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 2, 1, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 4, 5, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 2, 4, 3], [0, 1, 1, 0]]} "Class ", 4679, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 5, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 2, 4, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 4, 2, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 2, 1, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 4, 5, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 2, 4, 3], [1, 1, 1, 0]]} "Class ", 4680, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 5, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 2, 4, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 4, 2, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 2, 1, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 4, 5, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 2, 4, 3], [0, 0, 0, 1]]} "Class ", 4681, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 5, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 2, 4, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 2, 1, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 4, 5, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 2, 4, 3], [1, 0, 0, 1]]} "Class ", 4682, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 5, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 2, 4, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 4, 2, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 2, 1, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 4, 5, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 2, 4, 3], [0, 1, 0, 1]]} "Class ", 4683, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 5, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 2, 4, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 4, 2, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 2, 1, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 4, 5, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 2, 4, 3], [1, 1, 0, 1]]} "Class ", 4684, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 5, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 2, 4, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 4, 2, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 2, 1, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 4, 5, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 2, 4, 3], [0, 0, 1, 1]]} "Class ", 4685, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 5, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 2, 4, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 4, 2, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 2, 1, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 4, 5, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 2, 4, 3], [1, 0, 1, 1]]} "Class ", 4686, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 5, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 2, 4, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 4, 2, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 2, 1, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 4, 5, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 2, 4, 3], [0, 1, 1, 1]]} "Class ", 4687, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 5, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 2, 4, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 4, 2, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 2, 1, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 4, 5, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 2, 4, 3], [1, 1, 1, 1]]} "Class ", 4688, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 5, 1, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 1, 4, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 5, 2, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 1, 5, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 5, 1, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[2, 5, 1, 4, 3], [0, 0, 1, 0]]} "Class ", 4689, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 5, 1, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 1, 4, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 5, 2, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 1, 5, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 5, 1, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[2, 5, 1, 4, 3], [1, 0, 1, 0]]} "Class ", 4690, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 5, 1, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 1, 4, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 5, 2, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 1, 5, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 5, 1, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 5, 1, 4, 3], [0, 1, 1, 0]]} "Class ", 4691, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 5, 1, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 1, 4, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 5, 2, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 1, 5, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 5, 1, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 5, 1, 4, 3], [1, 1, 1, 0]]} "Class ", 4692, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 5, 1, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 1, 4, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 5, 2, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 1, 5, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 5, 1, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[2, 5, 1, 4, 3], [0, 0, 1, 1]]} "Class ", 4693, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 5, 1, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 1, 4, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 5, 2, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 1, 5, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 5, 1, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[2, 5, 1, 4, 3], [1, 0, 1, 1]]} "Class ", 4694, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 5, 1, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 1, 4, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 5, 2, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 1, 5, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 5, 1, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 5, 1, 4, 3], [0, 1, 1, 1]]} "Class ", 4695, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 5, 1, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 1, 4, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 5, 2, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 1, 5, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 5, 1, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 5, 1, 4, 3], [1, 1, 1, 1]]} "Class ", 4696, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 5, 4, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 1, 4, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 5, 2, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 1, 2, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 5, 4, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 2, 1, 4, 3], [0, 0, 1, 0]]} "Class ", 4697, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 5, 4, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 1, 4, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 5, 2, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 1, 2, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 5, 4, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 2, 1, 4, 3], [1, 0, 1, 0]]} "Class ", 4698, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 5, 4, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 1, 4, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 5, 2, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 1, 2, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 5, 4, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 2, 1, 4, 3], [0, 1, 1, 0]]} "Class ", 4699, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 5, 4, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 1, 4, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 5, 2, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 1, 2, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 5, 4, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 2, 1, 4, 3], [1, 1, 1, 0]]} "Class ", 4700, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 5, 4, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 1, 4, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 5, 2, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 1, 2, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 5, 4, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 2, 1, 4, 3], [0, 0, 1, 1]]} "Class ", 4701, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 5, 4, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 1, 4, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 5, 2, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 1, 2, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 5, 4, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 2, 1, 4, 3], [1, 0, 1, 1]]} "Class ", 4702, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 5, 4, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 1, 4, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 5, 2, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 1, 2, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 5, 4, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 2, 1, 4, 3], [0, 1, 1, 1]]} "Class ", 4703, " is:" {{[[1, 3, 2], [0, 1]], [[3, 2, 5, 4, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 1, 4, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 5, 2, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 4, 1, 2, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 2, 5, 4, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 2, 1, 4, 3], [1, 1, 1, 1]]} "Class ", 4704, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 5, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 1, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 5, 4, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 5, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 1, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 5, 4, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 401, 1311, 4375, 14842, 51032, 177443, 622863, 2204225, 7855594, 28169565, 101565203, 367969229, 1338934195, 4891033042] "" "Class ", 4705, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 5, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 1, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 5, 4, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 5, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 1, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 5, 4, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}] , [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1221, 3939, 12885, 42636, 142456, 479944, 1628631, 5561411, 19096541, 65896618, 228393724, 794741412, 2775388162] "" "Class ", 4706, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 5, 2, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 1, 4, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 5, 4, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 4, 5, 2, 3], [0, 1, 0, 0]]} "Class ", 4707, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 5, 2, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 1, 4, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 5, 4, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 4, 5, 2, 3], [1, 1, 0, 0]]} "Class ", 4708, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 5, 2, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 1, 4, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 5, 4, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 4, 5, 2, 3], [0, 0, 1, 0]]} "Class ", 4709, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 5, 2, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 1, 4, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 5, 4, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 5, 2, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 1, 4, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 5, 4, 1], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 4710, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 5, 2, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 1, 4, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 5, 4, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 4, 5, 2, 3], [0, 1, 1, 0]]} "Class ", 4711, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 5, 2, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 1, 4, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 5, 4, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 5, 2, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 1, 4, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 5, 4, 1], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 4712, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 5, 2, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 1, 4, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 5, 4, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 4, 5, 2, 3], [0, 0, 0, 1]]} "Class ", 4713, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 5, 2, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 1, 4, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 5, 4, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 4, 5, 2, 3], [1, 0, 0, 1]]} "Class ", 4714, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 5, 2, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 1, 4, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 5, 4, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 4, 5, 2, 3], [0, 1, 0, 1]]} "Class ", 4715, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 5, 2, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 1, 4, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 5, 4, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 4, 5, 2, 3], [1, 1, 0, 1]]} "Class ", 4716, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 5, 2, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 1, 4, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 5, 4, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 4, 5, 2, 3], [0, 0, 1, 1]]} "Class ", 4717, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 5, 2, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 1, 4, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 5, 4, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 4, 5, 2, 3], [1, 0, 1, 1]]} "Class ", 4718, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 5, 2, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 1, 4, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 5, 4, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 4, 5, 2, 3], [0, 1, 1, 1]]} "Class ", 4719, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 5, 2, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 1, 4, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 5, 4, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 1, 2, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 4, 5, 2, 3], [1, 1, 1, 1]]} "Class ", 4720, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 1, 5, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 5, 2, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 1, 4, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 5, 1, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 1, 5, 2], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 1, 5, 2, 3], [0, 1, 0, 0]]} "Class ", 4721, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 1, 5, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 5, 2, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 1, 4, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 5, 1, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 1, 5, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 1, 5, 2, 3], [1, 1, 0, 0]]} "Class ", 4722, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 1, 5, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 5, 2, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 1, 4, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 5, 1, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 1, 5, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 1, 5, 2, 3], [0, 1, 1, 0]]} "Class ", 4723, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 1, 5, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 5, 2, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 1, 4, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 5, 1, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 1, 5, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 1, 5, 2, 3], [1, 1, 1, 0]]} "Class ", 4724, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 1, 5, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 5, 2, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 1, 4, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 5, 1, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 1, 5, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 1, 5, 2, 3], [0, 1, 0, 1]]} "Class ", 4725, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 1, 5, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 5, 2, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 1, 4, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 5, 1, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 1, 5, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 1, 5, 2, 3], [1, 1, 0, 1]]} "Class ", 4726, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 1, 5, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 5, 2, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 1, 4, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 5, 1, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 1, 5, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 1, 5, 2, 3], [0, 1, 1, 1]]} "Class ", 4727, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 1, 5, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 5, 2, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 1, 4, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 5, 1, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 1, 5, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 1, 5, 2, 3], [1, 1, 1, 1]]} "Class ", 4728, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 5, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 5, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 401, 1311, 4375, 14842, 51032, 177443, 622863, 2204225, 7855594, 28169565, 101565203, 367969229, 1338934195, 4891033042] "" "Class ", 4729, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 5, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 5, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 4730, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 2, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 4, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 5, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 4, 2, 3], [0, 1, 0, 0]]} "Class ", 4731, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 2, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 4, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 5, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 2, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 4, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 5, 1], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [3, 4, 1, 2, 5], {3, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1033, 2986, 8594, 24674, 70757, 202814, 581272, 1666003, 4775323, 13688536, 39240095, 112490042, 322480613] "" "Class ", 4732, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 2, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 4, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 5, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 4, 2, 3], [0, 0, 1, 0]]} "Class ", 4733, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 2, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 4, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 5, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 2, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 4, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 5, 1], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [3, 4, 1, 2, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 4734, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 2, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 4, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 5, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 4, 2, 3], [0, 1, 1, 0]]} "Class ", 4735, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 2, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 4, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 5, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 2, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 4, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 5, 1], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [3, 4, 1, 2, 5], {3, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1033, 2986, 8594, 24674, 70757, 202814, 581272, 1666003, 4775323, 13688536, 39240095, 112490042, 322480613] "" "Class ", 4736, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 2, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 4, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 5, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 4, 2, 3], [0, 0, 0, 1]]} "Class ", 4737, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 4, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 5, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]} "Class ", 4738, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 2, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 4, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 5, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 4, 2, 3], [0, 1, 0, 1]]} "Class ", 4739, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 2, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 4, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 5, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 5, 4, 2, 3], [1, 1, 0, 1]]} "Class ", 4740, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 2, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 4, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 5, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 4, 2, 3], [0, 0, 1, 1]]} "Class ", 4741, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 2, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 4, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 5, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 5, 4, 2, 3], [1, 0, 1, 1]]} "Class ", 4742, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 2, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 4, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 5, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 4, 2, 3], [0, 1, 1, 1]]} "Class ", 4743, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 2, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 4, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 5, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 2, 1, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 5, 4, 2, 3], [1, 1, 1, 1]]} "Class ", 4744, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 4, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 2, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 1, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 2, 5, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 4, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 2, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 1, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 4, 2, 5, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 394, 1273, 4194, 14039, 47614, 163266, 565072, 1971476, 6926313, 24482914, 87009495, 310710172, 1114326403, 4011922558] "" "Class ", 4745, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 4, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 2, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 1, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 2, 5, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 4, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 2, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 1, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 4, 2, 5, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [ [2, 3, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1220, 3929, 12822, 42309, 140922, 473169, 1599864, 5442561, 18615176, 63975857, 220816906, 765121477, 2660426630] "" "Class ", 4746, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 5, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 4, 2, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 2, 4, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 1, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 2, 5, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 4, 2, 3], [0, 1, 0, 0]]} "Class ", 4747, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 5, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 4, 2, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 2, 4, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 1, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 2, 5, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 4, 2, 3], [1, 1, 0, 0]]} "Class ", 4748, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 5, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 4, 2, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 2, 4, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 1, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 2, 5, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 4, 2, 3], [0, 0, 1, 0]]} "Class ", 4749, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 5, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 4, 2, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 2, 4, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 1, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 2, 5, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 4, 2, 3], [1, 0, 1, 0]]} "Class ", 4750, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 5, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 4, 2, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 2, 4, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 1, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 2, 5, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 4, 2, 3], [0, 1, 1, 0]]} "Class ", 4751, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 5, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 4, 2, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 2, 4, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 1, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 2, 5, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 4, 2, 3], [1, 1, 1, 0]]} "Class ", 4752, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 5, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 4, 2, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 2, 4, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 1, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 2, 5, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 4, 2, 3], [0, 0, 0, 1]]} "Class ", 4753, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 5, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 4, 2, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 2, 4, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 1, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 2, 5, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 4, 2, 3], [1, 0, 0, 1]]} "Class ", 4754, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 5, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 4, 2, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 2, 4, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 1, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 2, 5, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 4, 2, 3], [0, 1, 0, 1]]} "Class ", 4755, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 5, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 4, 2, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 2, 4, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 1, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 2, 5, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 4, 2, 3], [1, 1, 0, 1]]} "Class ", 4756, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 5, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 4, 2, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 2, 4, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 1, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 2, 5, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 4, 2, 3], [0, 0, 1, 1]]} "Class ", 4757, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 5, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 4, 2, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 2, 4, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 1, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 2, 5, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 4, 2, 3], [1, 0, 1, 1]]} "Class ", 4758, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 5, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 4, 2, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 2, 4, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 1, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 2, 5, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 4, 2, 3], [0, 1, 1, 1]]} "Class ", 4759, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 5, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 4, 2, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 2, 4, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 4, 1, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 2, 5, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 4, 2, 3], [1, 1, 1, 1]]} "Class ", 4760, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 4, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1267, 4166, 13918, 47109, 161205, 556783, 1938487, 6796031, 23971361, 85009671, 302918609, 1084049439, 3894514424] "" "Class ", 4761, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1212, 3885, 12614, 41400, 137132, 457841, 1539150, 5205612, 17700450, 60473476, 207491052, 714668954, 2470156910] "" "Class ", 4762, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 4, 1, 5], {1, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 4763, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 2, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 4, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 2, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 4, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 4764, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 2, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 4, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 5, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[4, 5, 1, 2, 3], [0, 0, 1, 0]]} "Class ", 4765, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 2, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 4, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 5, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[4, 5, 1, 2, 3], [1, 0, 1, 0]]} "Class ", 4766, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 4, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 5, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 1, 0]]} "Class ", 4767, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 2, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 4, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 5, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 5, 1, 2, 3], [1, 1, 1, 0]]} "Class ", 4768, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 4, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 5, 4], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]} "Class ", 4769, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 2, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 4, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 5, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[4, 5, 1, 2, 3], [1, 0, 0, 1]]} "Class ", 4770, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 5, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]} "Class ", 4771, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 2, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 4, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 5, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 5, 1, 2, 3], [1, 1, 0, 1]]} "Class ", 4772, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 2, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 4, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 5, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[4, 5, 1, 2, 3], [0, 0, 1, 1]]} "Class ", 4773, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 2, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 4, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 5, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[4, 5, 1, 2, 3], [1, 0, 1, 1]]} "Class ", 4774, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 4, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 5, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]} "Class ", 4775, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 2, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 4, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 5, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 5, 1, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 5, 1, 2, 3], [1, 1, 1, 1]]} "Class ", 4776, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 4, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1210, 3867, 12504, 40833, 134482, 446197, 1490068, 5004702, 16895480, 57299652, 195130472, 666990671, 2287644406] "" "Class ", 4777, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 4778, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [0, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [0, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 4, 1, 5], {1, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 4779, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}], [ [2, 3, 4, 1, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 4780, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 2, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 4, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 4, 1, 2, 3], [0, 0, 1, 0]]} "Class ", 4781, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 2, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 4, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 4, 1, 2, 3], [1, 0, 1, 0]]} "Class ", 4782, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 4, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 0]]} "Class ", 4783, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 4, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 4, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]} "Class ", 4784, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 4, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 4, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]} "Class ", 4785, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 4, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]} "Class ", 4786, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]} "Class ", 4787, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]} "Class ", 4788, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 2, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 4, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 4, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 4, 1, 2, 3], [0, 0, 1, 1]]} "Class ", 4789, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 2, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 4, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 4, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 4, 1, 2, 3], [1, 0, 1, 1]]} "Class ", 4790, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 4, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]} "Class ", 4791, " is:" {{[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 4, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 4, 5, 2, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]} "Class ", 4792, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 1, 2, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 5, 1, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 1, 5, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 5, 4, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 1, 2, 4], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[2, 4, 5, 1, 3], [0, 0, 0, 1]]} "Class ", 4793, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 1, 2, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 5, 1, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 1, 5, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 5, 4, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 1, 2, 4], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[2, 4, 5, 1, 3], [1, 0, 0, 1]]} "Class ", 4794, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 1, 2, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 5, 1, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 1, 5, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 5, 4, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 1, 2, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 4, 5, 1, 3], [0, 1, 0, 1]]} "Class ", 4795, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 1, 2, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 5, 1, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 1, 5, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 5, 4, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 1, 2, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 4, 5, 1, 3], [1, 1, 0, 1]]} "Class ", 4796, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 1, 2, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 5, 1, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 1, 5, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 5, 4, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 1, 2, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[2, 4, 5, 1, 3], [0, 0, 1, 1]]} "Class ", 4797, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 1, 2, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 5, 1, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 1, 5, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 5, 4, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 1, 2, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[2, 4, 5, 1, 3], [1, 0, 1, 1]]} "Class ", 4798, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 1, 2, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 5, 1, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 1, 5, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 5, 4, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 1, 2, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 4, 5, 1, 3], [0, 1, 1, 1]]} "Class ", 4799, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 1, 2, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 5, 1, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 1, 5, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 5, 4, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 1, 2, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 4, 5, 1, 3], [1, 1, 1, 1]]} "Class ", 4800, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 1, 4, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 5, 1, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 1, 5, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 5, 2, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 1, 4, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 2, 5, 1, 3], [0, 1, 0, 1]]} "Class ", 4801, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 1, 4, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 5, 1, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 1, 5, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 5, 2, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 1, 4, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 2, 5, 1, 3], [1, 1, 0, 1]]} "Class ", 4802, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 1, 4, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 5, 1, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 1, 5, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 5, 2, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 1, 4, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 2, 5, 1, 3], [0, 1, 1, 1]]} "Class ", 4803, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 1, 4, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 5, 1, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 1, 5, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 5, 2, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 1, 4, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 2, 5, 1, 3], [1, 1, 1, 1]]} "Class ", 4804, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 2, 1, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 4, 1, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 2, 5, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 4, 5, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 2, 1, 4], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[2, 5, 4, 1, 3], [0, 0, 0, 1]]} "Class ", 4805, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 2, 1, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 4, 1, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 2, 5, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 4, 5, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 2, 1, 4], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[2, 5, 4, 1, 3], [1, 0, 0, 1]]} "Class ", 4806, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 2, 1, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 4, 1, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 2, 5, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 4, 5, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 2, 1, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 5, 4, 1, 3], [0, 1, 0, 1]]} "Class ", 4807, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 2, 1, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 4, 1, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 2, 5, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 4, 5, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 2, 1, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 5, 4, 1, 3], [1, 1, 0, 1]]} "Class ", 4808, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 2, 1, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 4, 1, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 2, 5, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 4, 5, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 2, 1, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[2, 5, 4, 1, 3], [0, 0, 1, 1]]} "Class ", 4809, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 2, 1, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 4, 1, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 2, 5, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 4, 5, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 2, 1, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[2, 5, 4, 1, 3], [1, 0, 1, 1]]} "Class ", 4810, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 2, 1, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 4, 1, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 2, 5, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 4, 5, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 2, 1, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 5, 4, 1, 3], [0, 1, 1, 1]]} "Class ", 4811, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 2, 1, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 4, 1, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 2, 5, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 4, 5, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 2, 1, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 5, 4, 1, 3], [1, 1, 1, 1]]} "Class ", 4812, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 2, 4, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 2, 5, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 4, 2, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 2, 4, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 1]]} "Class ", 4813, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 2, 4, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 2, 5, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 4, 2, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 2, 4, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 1]]} "Class ", 4814, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 2, 4, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 4, 1, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 2, 5, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 4, 2, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 2, 4, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 2, 4, 1, 3], [0, 1, 0, 1]]} "Class ", 4815, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 2, 4, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 4, 1, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 2, 5, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 4, 2, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 2, 4, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 2, 4, 1, 3], [1, 1, 0, 1]]} "Class ", 4816, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 2, 4, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 4, 1, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 2, 5, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 4, 2, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 2, 4, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 2, 4, 1, 3], [0, 0, 1, 1]]} "Class ", 4817, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 2, 4, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 4, 1, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 2, 5, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 4, 2, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 2, 4, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 2, 4, 1, 3], [1, 0, 1, 1]]} "Class ", 4818, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 2, 4, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 4, 1, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 2, 5, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 4, 2, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 2, 4, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 2, 4, 1, 3], [0, 1, 1, 1]]} "Class ", 4819, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 2, 4, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 4, 1, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 2, 5, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 4, 2, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 2, 4, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 2, 4, 1, 3], [1, 1, 1, 1]]} "Class ", 4820, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 4, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 4, 5, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 2, 5, 4], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 4, 1, 2], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]} "Class ", 4821, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 4, 1, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 2, 1, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 4, 5, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 2, 5, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 4, 1, 2], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[4, 5, 2, 1, 3], [1, 0, 0, 1]]} "Class ", 4822, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 4, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 2, 5, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 4, 1, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]} "Class ", 4823, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 4, 1, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 2, 1, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 4, 5, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 2, 5, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 4, 1, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 5, 2, 1, 3], [1, 1, 0, 1]]} "Class ", 4824, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 4, 1, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 2, 1, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 4, 5, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 2, 5, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 4, 1, 2], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[4, 5, 2, 1, 3], [0, 0, 1, 1]]} "Class ", 4825, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 4, 1, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 2, 1, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 4, 5, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 2, 5, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 4, 1, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[4, 5, 2, 1, 3], [1, 0, 1, 1]]} "Class ", 4826, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 4, 1, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 4, 5, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 2, 5, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 4, 1, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]} "Class ", 4827, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 4, 1, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 2, 1, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 4, 5, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 2, 5, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 4, 1, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 5, 2, 1, 3], [1, 1, 1, 1]]} "Class ", 4828, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 2, 4, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]} "Class ", 4829, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 2, 4, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]} "Class ", 4830, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 2, 4, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]} "Class ", 4831, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 2, 4, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]} "Class ", 4832, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 4, 2, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 2, 1, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 4, 5, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 2, 4, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 4, 2, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 4, 2, 1, 3], [0, 0, 1, 1]]} "Class ", 4833, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 4, 2, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 2, 1, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 4, 5, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 2, 4, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 4, 2, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 4, 2, 1, 3], [1, 0, 1, 1]]} "Class ", 4834, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 4, 2, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 2, 1, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 4, 5, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 2, 4, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 4, 2, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 4, 2, 1, 3], [0, 1, 1, 1]]} "Class ", 4835, " is:" {{[[1, 3, 2], [0, 1]], [[3, 5, 4, 2, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 2, 1, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 4, 5, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 2, 4, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 5, 4, 2, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 4, 2, 1, 3], [1, 1, 1, 1]]} "Class ", 4836, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 2, 3, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 4, 3, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 2, 3, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 1, 2, 3, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 4, 3, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 1, 2, 3, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 1, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}] , [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 127, 408, 1346, 4533, 15518, 53837, 188864, 668802, 2387503, 8582691, 31042653, 112885776, 412482587, 1513699914, 5576428245] "" "Class ", 4837, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 2, 3, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 4, 3, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 2, 3, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 1, 2, 3, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 4, 3, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 1, 2, 3, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [4, 1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4158, 13873, 46893, 160247, 552723, 1921756, 6728347, 23701026, 83939765, 298712615, 1067598164, 3830414563] "" "Class ", 4838, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 2, 3, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 4, 5, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 2, 1, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 4, 3, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 2, 3, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 3, 4, 5, 2], [0, 1, 0, 0]]} "Class ", 4839, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 2, 3, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 4, 5, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 2, 1, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 4, 3, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 2, 3, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 3, 4, 5, 2], [1, 1, 0, 0]]} "Class ", 4840, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 2, 3, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 4, 5, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 2, 1, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 4, 3, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 2, 3, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 3, 4, 5, 2], [0, 0, 1, 0]]} "Class ", 4841, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 2, 3, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 4, 5, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 2, 1, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 4, 3, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 2, 3, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 3, 4, 5, 2], [1, 0, 1, 0]]} "Class ", 4842, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 2, 3, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 4, 5, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 2, 1, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 4, 3, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 2, 3, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 3, 4, 5, 2], [0, 1, 1, 0]]} "Class ", 4843, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 2, 3, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 4, 5, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 2, 1, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 4, 3, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 2, 3, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 3, 4, 5, 2], [1, 1, 1, 0]]} "Class ", 4844, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 2, 3, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 4, 3, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 2, 3, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]} "Class ", 4845, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 2, 3, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 4, 3, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 2, 3, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]} "Class ", 4846, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 2, 3, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 4, 5, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 2, 1, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 4, 3, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 2, 3, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 3, 4, 5, 2], [0, 1, 0, 1]]} "Class ", 4847, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 2, 3, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 4, 5, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 2, 1, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 4, 3, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 2, 3, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 3, 4, 5, 2], [1, 1, 0, 1]]} "Class ", 4848, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 2, 3, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 4, 5, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 2, 1, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 4, 3, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 2, 3, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 3, 4, 5, 2], [0, 0, 1, 1]]} "Class ", 4849, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 2, 3, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 4, 5, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 2, 1, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 4, 3, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 2, 3, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 3, 4, 5, 2], [1, 0, 1, 1]]} "Class ", 4850, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 2, 3, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 4, 5, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 2, 1, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 4, 3, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 2, 3, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 3, 4, 5, 2], [0, 1, 1, 1]]} "Class ", 4851, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 2, 3, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 4, 5, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 2, 1, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 4, 3, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 2, 3, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 3, 4, 5, 2], [1, 1, 1, 1]]} "Class ", 4852, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 2, 5, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 4, 5, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 2, 1, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 4, 1, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 2, 5, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 1, 4, 5, 2], [0, 1, 0, 0]]} "Class ", 4853, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 2, 5, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 4, 5, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 2, 1, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 4, 1, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 2, 5, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[3, 1, 4, 5, 2], [1, 1, 0, 0]]} "Class ", 4854, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 2, 5, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 4, 5, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 2, 1, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 4, 1, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 2, 5, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 1, 4, 5, 2], [0, 1, 1, 0]]} "Class ", 4855, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 2, 5, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 4, 5, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 2, 1, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 4, 1, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 2, 5, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[3, 1, 4, 5, 2], [1, 1, 1, 0]]} "Class ", 4856, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 2, 5, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 4, 5, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 2, 1, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 4, 1, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 2, 5, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 1, 4, 5, 2], [0, 1, 0, 1]]} "Class ", 4857, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 2, 5, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 4, 5, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 2, 1, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 4, 1, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 2, 5, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[3, 1, 4, 5, 2], [1, 1, 0, 1]]} "Class ", 4858, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 2, 5, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 4, 5, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 2, 1, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 4, 1, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 2, 5, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 1, 4, 5, 2], [0, 1, 1, 1]]} "Class ", 4859, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 2, 5, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 4, 5, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 2, 1, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 4, 1, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 2, 5, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[3, 1, 4, 5, 2], [1, 1, 1, 1]]} "Class ", 4860, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 3, 2, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 3, 5, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 3, 1, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 3, 4, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 3, 2, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 4, 3, 5, 2], [0, 0, 1, 0]]} "Class ", 4861, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 3, 2, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 3, 5, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 3, 1, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 3, 4, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 3, 2, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 4, 3, 5, 2], [1, 0, 1, 0]]} "Class ", 4862, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 3, 2, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 3, 5, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 3, 1, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 3, 4, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 3, 2, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 4, 3, 5, 2], [0, 1, 1, 0]]} "Class ", 4863, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 3, 2, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 3, 5, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 3, 1, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 3, 4, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 3, 2, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 4, 3, 5, 2], [1, 1, 1, 0]]} "Class ", 4864, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 3, 2, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 3, 5, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 3, 1, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 3, 4, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 3, 2, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 4, 3, 5, 2], [0, 0, 1, 1]]} "Class ", 4865, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 3, 2, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 3, 5, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 3, 1, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 3, 4, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 3, 2, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 4, 3, 5, 2], [1, 0, 1, 1]]} "Class ", 4866, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 3, 2, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 3, 5, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 3, 1, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 3, 4, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 3, 2, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 4, 3, 5, 2], [0, 1, 1, 1]]} "Class ", 4867, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 3, 2, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 3, 5, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 3, 1, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 3, 4, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 3, 2, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 4, 3, 5, 2], [1, 1, 1, 1]]} "Class ", 4868, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 3, 5, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 3, 5, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 3, 1, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 3, 1, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 3, 5, 2], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[4, 1, 3, 5, 2], [0, 0, 1, 0]]} "Class ", 4869, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 3, 5, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 3, 5, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 3, 1, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 3, 1, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 3, 5, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[4, 1, 3, 5, 2], [1, 0, 1, 0]]} "Class ", 4870, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 3, 5, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 3, 5, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 3, 1, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 3, 1, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 3, 5, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 1, 3, 5, 2], [0, 1, 1, 0]]} "Class ", 4871, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 3, 5, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 3, 5, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 3, 1, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 3, 1, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 3, 5, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 1, 3, 5, 2], [1, 1, 1, 0]]} "Class ", 4872, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 3, 5, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 3, 5, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 3, 1, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 3, 1, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 3, 5, 2], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[4, 1, 3, 5, 2], [0, 0, 1, 1]]} "Class ", 4873, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 3, 5, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 3, 5, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 3, 1, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 3, 1, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 3, 5, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[4, 1, 3, 5, 2], [1, 0, 1, 1]]} "Class ", 4874, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 3, 5, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 3, 5, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 3, 1, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 3, 1, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 3, 5, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 1, 3, 5, 2], [0, 1, 1, 1]]} "Class ", 4875, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 3, 5, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 3, 5, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 3, 1, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 3, 1, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 3, 5, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 1, 3, 5, 2], [1, 1, 1, 1]]} "Class ", 4876, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 5, 2, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 1, 5, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 5, 1, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 1, 4, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 5, 2, 3], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[3, 4, 1, 5, 2], [0, 0, 1, 0]]} "Class ", 4877, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 5, 2, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 1, 5, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 5, 1, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 1, 4, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 5, 2, 3], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[3, 4, 1, 5, 2], [1, 0, 1, 0]]} "Class ", 4878, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 5, 2, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 1, 5, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 5, 1, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 1, 4, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 5, 2, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 4, 1, 5, 2], [0, 1, 1, 0]]} "Class ", 4879, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 5, 2, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 1, 5, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 5, 1, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 1, 4, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 5, 2, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[3, 4, 1, 5, 2], [1, 1, 1, 0]]} "Class ", 4880, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 5, 2, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 1, 5, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 5, 1, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 1, 4, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 5, 2, 3], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[3, 4, 1, 5, 2], [0, 0, 1, 1]]} "Class ", 4881, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 5, 2, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 1, 5, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 5, 1, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 1, 4, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 5, 2, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[3, 4, 1, 5, 2], [1, 0, 1, 1]]} "Class ", 4882, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 5, 2, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 1, 5, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 5, 1, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 1, 4, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 5, 2, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 4, 1, 5, 2], [0, 1, 1, 1]]} "Class ", 4883, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 5, 2, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 1, 5, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 5, 1, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 1, 4, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 5, 2, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[3, 4, 1, 5, 2], [1, 1, 1, 1]]} "Class ", 4884, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 5, 3, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 1, 5, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 5, 1, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 1, 3, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 5, 3, 2], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[4, 3, 1, 5, 2], [0, 0, 1, 0]]} "Class ", 4885, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 5, 3, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 1, 5, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 5, 1, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 1, 3, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 5, 3, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[4, 3, 1, 5, 2], [1, 0, 1, 0]]} "Class ", 4886, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 5, 3, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 1, 5, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 5, 1, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 1, 3, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 5, 3, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 3, 1, 5, 2], [0, 1, 1, 0]]} "Class ", 4887, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 5, 3, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 1, 5, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 5, 1, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 1, 3, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 5, 3, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 3, 1, 5, 2], [1, 1, 1, 0]]} "Class ", 4888, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 5, 3, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 1, 5, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 5, 1, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 1, 3, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 5, 3, 2], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[4, 3, 1, 5, 2], [0, 0, 1, 1]]} "Class ", 4889, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 5, 3, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 1, 5, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 5, 1, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 1, 3, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 5, 3, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[4, 3, 1, 5, 2], [1, 0, 1, 1]]} "Class ", 4890, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 5, 3, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 1, 5, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 5, 1, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 1, 3, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 5, 3, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 3, 1, 5, 2], [0, 1, 1, 1]]} "Class ", 4891, " is:" {{[[1, 3, 2], [0, 1]], [[4, 1, 5, 3, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 1, 5, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 5, 1, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 5, 1, 3, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 1, 5, 3, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 3, 1, 5, 2], [1, 1, 1, 1]]} "Class ", 4892, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 1, 3, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 5, 4, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 5, 3, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 1, 3, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 2, 1, 3, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 5, 4, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 5, 3, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 2, 1, 3, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [[4, 2, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}] , [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 127, 408, 1346, 4533, 15518, 53837, 188864, 668802, 2387503, 8582691, 31042653, 112885776, 412482587, 1513699914, 5576428245] "" "Class ", 4893, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 1, 3, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 5, 4, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 5, 3, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 1, 3, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 2, 1, 3, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 5, 4, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 5, 3, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 2, 1, 3, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [4, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4158, 13873, 46893, 160247, 552723, 1921756, 6728347, 23701026, 83939765, 298712615, 1067598164, 3830414563] "" "Class ", 4894, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 1, 3, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 5, 4, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 1, 2, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 5, 3, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 1, 3, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 3, 5, 4, 2], [0, 1, 0, 0]]} "Class ", 4895, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 1, 3, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 5, 4, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 1, 2, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 5, 3, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 1, 3, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 3, 5, 4, 2], [1, 1, 0, 0]]} "Class ", 4896, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 1, 3, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 5, 4, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 1, 2, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 5, 3, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 1, 3, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 3, 5, 4, 2], [0, 0, 1, 0]]} "Class ", 4897, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 1, 3, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 5, 4, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 1, 2, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 5, 3, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 1, 3, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 3, 5, 4, 2], [1, 0, 1, 0]]} "Class ", 4898, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 1, 3, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 5, 4, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 1, 2, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 5, 3, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 1, 3, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 3, 5, 4, 2], [0, 1, 1, 0]]} "Class ", 4899, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 1, 3, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 5, 4, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 1, 2, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 5, 3, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 1, 3, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 3, 5, 4, 2], [1, 1, 1, 0]]} "Class ", 4900, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 1, 3, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 5, 4, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 5, 3, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 1, 3, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 3, 5, 4, 2], [0, 0, 0, 1]]} "Class ", 4901, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 1, 3, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 5, 4, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 5, 3, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 1, 3, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 3, 5, 4, 2], [1, 0, 0, 1]]} "Class ", 4902, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 1, 3, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 5, 4, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 1, 2, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 5, 3, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 1, 3, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 3, 5, 4, 2], [0, 1, 0, 1]]} "Class ", 4903, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 1, 3, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 5, 4, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 1, 2, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 5, 3, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 1, 3, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 3, 5, 4, 2], [1, 1, 0, 1]]} "Class ", 4904, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 1, 3, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 5, 4, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 1, 2, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 5, 3, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 1, 3, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 3, 5, 4, 2], [0, 0, 1, 1]]} "Class ", 4905, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 1, 3, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 5, 4, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 1, 2, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 5, 3, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 1, 3, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 3, 5, 4, 2], [1, 0, 1, 1]]} "Class ", 4906, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 1, 3, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 5, 4, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 1, 2, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 5, 3, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 1, 3, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 3, 5, 4, 2], [0, 1, 1, 1]]} "Class ", 4907, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 1, 3, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 3, 5, 4, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 3, 1, 2, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 5, 3, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 1, 3, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 3, 5, 4, 2], [1, 1, 1, 1]]} "Class ", 4908, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 1, 5, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 5, 4, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 1, 2, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 5, 1, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 1, 5, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 1, 5, 4, 2], [0, 1, 0, 0]]} "Class ", 4909, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 1, 5, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 5, 4, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 1, 2, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 5, 1, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 1, 5, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[3, 1, 5, 4, 2], [1, 1, 0, 0]]} "Class ", 4910, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 1, 5, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 5, 4, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 1, 2, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 5, 1, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 1, 5, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 1, 5, 4, 2], [0, 1, 1, 0]]} "Class ", 4911, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 1, 5, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 5, 4, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 1, 2, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 5, 1, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 1, 5, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[3, 1, 5, 4, 2], [1, 1, 1, 0]]} "Class ", 4912, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 1, 5, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 5, 4, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 1, 2, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 5, 1, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 1, 5, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 1, 5, 4, 2], [0, 1, 0, 1]]} "Class ", 4913, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 1, 5, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 5, 4, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 1, 2, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 5, 1, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 1, 5, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[3, 1, 5, 4, 2], [1, 1, 0, 1]]} "Class ", 4914, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 1, 5, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 5, 4, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 1, 2, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 5, 1, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 1, 5, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 1, 5, 4, 2], [0, 1, 1, 1]]} "Class ", 4915, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 1, 5, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 5, 4, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 5, 1, 2, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 5, 1, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 1, 5, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[3, 1, 5, 4, 2], [1, 1, 1, 1]]} "Class ", 4916, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 3, 4, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 3, 2, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 3, 5, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 3, 1, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 3, 4, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 3, 2, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 3, 5, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 2, 3, 1, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}] , [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 127, 408, 1346, 4533, 15518, 53837, 188864, 668802, 2387503, 8582691, 31042653, 112885776, 412482587, 1513699914, 5576428245] "" "Class ", 4917, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 3, 4, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 3, 2, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 3, 5, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 3, 1, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 3, 4, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 3, 2, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 3, 5, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 2, 3, 1, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1220, 3929, 12822, 42309, 140922, 473169, 1599864, 5442561, 18615176, 63975857, 220816906, 765121477, 2660426630] "" "Class ", 4918, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 1, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 3, 4, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 3, 2, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 3, 5, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 3, 1, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 3, 4, 2], [0, 1, 0, 0]]} "Class ", 4919, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 1, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 3, 4, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 3, 2, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 3, 5, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 3, 1, 5], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 1, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 3, 4, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 3, 2, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 3, 5, 1], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 2, 3, 1, 5], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 366, 1106, 3367, 10324, 31865, 98930, 308737, 967904, 3046747, 9625304, 30507667, 96980798, 309121448, 987731324] "" "Class ", 4920, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 1, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 3, 4, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 3, 2, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 3, 5, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 3, 1, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 3, 4, 2], [0, 0, 1, 0]]} "Class ", 4921, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 1, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 3, 4, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 3, 2, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 3, 5, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 3, 1, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 5, 3, 4, 2], [1, 0, 1, 0]]} "Class ", 4922, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 1, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 3, 4, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 3, 2, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 3, 5, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 3, 1, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 3, 4, 2], [0, 1, 1, 0]]} "Class ", 4923, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 1, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 3, 4, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 3, 2, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 3, 5, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 3, 1, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 5, 3, 4, 2], [1, 1, 1, 0]]} "Class ", 4924, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 1, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 3, 4, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 3, 2, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 3, 5, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 3, 1, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 3, 4, 2], [0, 0, 0, 1]]} "Class ", 4925, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 1, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 3, 4, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 3, 2, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 3, 5, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 3, 1, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 5, 3, 4, 2], [1, 0, 0, 1]]} "Class ", 4926, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 1, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 3, 4, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 3, 2, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 3, 5, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 3, 1, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 3, 4, 2], [0, 1, 0, 1]]} "Class ", 4927, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 1, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 3, 4, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 3, 2, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 3, 5, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 3, 1, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 5, 3, 4, 2], [1, 1, 0, 1]]} "Class ", 4928, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 1, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 3, 4, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 3, 2, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 3, 5, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 3, 1, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 3, 4, 2], [0, 0, 1, 1]]} "Class ", 4929, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 1, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 3, 4, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 3, 2, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 3, 5, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 3, 1, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 5, 3, 4, 2], [1, 0, 1, 1]]} "Class ", 4930, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 1, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 3, 4, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 3, 2, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 3, 5, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 3, 1, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 3, 4, 2], [0, 1, 1, 1]]} "Class ", 4931, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 1, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 3, 4, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 3, 2, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 3, 5, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 3, 1, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 5, 3, 4, 2], [1, 1, 1, 1]]} "Class ", 4932, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 3, 4, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 3, 2, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 3, 1, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 3, 5, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 3, 4, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 3, 2, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 3, 1, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 2, 3, 5, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 1, 0, 0]}], [[3, 1, 2, 4, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 3, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 401, 1311, 4376, 14850, 51077, 177660, 623833, 2208378, 7872910, 28240520, 101852500, 369122649, 1343536175, 4909309244] "" "Class ", 4933, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 3, 4, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 3, 2, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 3, 1, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 3, 5, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 3, 4, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 3, 2, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 3, 1, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 2, 3, 5, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4158, 13873, 46893, 160247, 552723, 1921756, 6728347, 23701026, 83939765, 298712615, 1067598164, 3830414563] "" "Class ", 4934, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 5, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 3, 4, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 3, 2, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 3, 1, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 3, 5, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 3, 4, 2], [0, 1, 0, 0]]} "Class ", 4935, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 5, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 3, 4, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 3, 2, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 3, 1, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 3, 5, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 3, 4, 2], [1, 1, 0, 0]]} "Class ", 4936, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 5, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 3, 4, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 3, 2, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 3, 1, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 3, 5, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 3, 4, 2], [0, 0, 1, 0]]} "Class ", 4937, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 5, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 3, 4, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 3, 2, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 3, 1, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 3, 5, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 3, 4, 2], [1, 0, 1, 0]]} "Class ", 4938, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 5, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 3, 4, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 3, 2, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 3, 1, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 3, 5, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 3, 4, 2], [0, 1, 1, 0]]} "Class ", 4939, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 5, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 3, 4, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 3, 2, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 3, 1, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 3, 5, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 3, 4, 2], [1, 1, 1, 0]]} "Class ", 4940, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 5, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 3, 4, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 3, 2, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 3, 1, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 3, 5, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 3, 4, 2], [0, 0, 0, 1]]} "Class ", 4941, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 5, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 3, 4, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 3, 2, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 3, 1, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 3, 5, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 3, 4, 2], [1, 0, 0, 1]]} "Class ", 4942, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 5, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 3, 4, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 3, 2, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 3, 1, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 3, 5, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 3, 4, 2], [0, 1, 0, 1]]} "Class ", 4943, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 5, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 3, 4, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 3, 2, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 3, 1, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 3, 5, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 3, 4, 2], [1, 1, 0, 1]]} "Class ", 4944, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 5, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 3, 4, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 3, 2, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 3, 1, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 3, 5, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 3, 4, 2], [0, 0, 1, 1]]} "Class ", 4945, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 5, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 3, 4, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 3, 2, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 3, 1, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 3, 5, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 3, 4, 2], [1, 0, 1, 1]]} "Class ", 4946, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 5, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 3, 4, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 3, 2, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 3, 1, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 3, 5, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 3, 4, 2], [0, 1, 1, 1]]} "Class ", 4947, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 5, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 3, 4, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 3, 2, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 3, 1, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 3, 5, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 3, 4, 2], [1, 1, 1, 1]]} "Class ", 4948, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 5, 1, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 1, 4, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 5, 2, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 1, 5, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 5, 1, 3], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[3, 5, 1, 4, 2], [0, 0, 1, 0]]} "Class ", 4949, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 5, 1, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 1, 4, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 5, 2, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 1, 5, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 5, 1, 3], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[3, 5, 1, 4, 2], [1, 0, 1, 0]]} "Class ", 4950, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 5, 1, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 1, 4, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 5, 2, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 1, 5, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 5, 1, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 5, 1, 4, 2], [0, 1, 1, 0]]} "Class ", 4951, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 5, 1, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 1, 4, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 5, 2, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 1, 5, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 5, 1, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[3, 5, 1, 4, 2], [1, 1, 1, 0]]} "Class ", 4952, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 5, 1, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 1, 4, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 5, 2, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 1, 5, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 5, 1, 3], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[3, 5, 1, 4, 2], [0, 0, 1, 1]]} "Class ", 4953, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 5, 1, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 1, 4, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 5, 2, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 1, 5, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 5, 1, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[3, 5, 1, 4, 2], [1, 0, 1, 1]]} "Class ", 4954, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 5, 1, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 1, 4, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 5, 2, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 1, 5, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 5, 1, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 5, 1, 4, 2], [0, 1, 1, 1]]} "Class ", 4955, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 5, 1, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 1, 4, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 5, 2, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 1, 5, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 5, 1, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[3, 5, 1, 4, 2], [1, 1, 1, 1]]} "Class ", 4956, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 5, 3, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 1, 4, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 5, 2, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 1, 3, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 5, 3, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 3, 1, 4, 2], [0, 0, 1, 0]]} "Class ", 4957, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 5, 3, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 1, 4, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 5, 2, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 1, 3, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 5, 3, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 3, 1, 4, 2], [1, 0, 1, 0]]} "Class ", 4958, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 5, 3, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 1, 4, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 5, 2, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 1, 3, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 5, 3, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 3, 1, 4, 2], [0, 1, 1, 0]]} "Class ", 4959, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 5, 3, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 1, 4, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 5, 2, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 1, 3, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 5, 3, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 3, 1, 4, 2], [1, 1, 1, 0]]} "Class ", 4960, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 5, 3, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 1, 4, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 5, 2, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 1, 3, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 5, 3, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 3, 1, 4, 2], [0, 0, 1, 1]]} "Class ", 4961, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 5, 3, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 1, 4, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 5, 2, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 1, 3, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 5, 3, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 3, 1, 4, 2], [1, 0, 1, 1]]} "Class ", 4962, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 5, 3, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 1, 4, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 5, 2, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 1, 3, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 5, 3, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 3, 1, 4, 2], [0, 1, 1, 1]]} "Class ", 4963, " is:" {{[[1, 3, 2], [0, 1]], [[4, 2, 5, 3, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 1, 4, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 5, 2, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 4, 1, 3, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 2, 5, 3, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 3, 1, 4, 2], [1, 1, 1, 1]]} "Class ", 4964, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 1, 2, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 5, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 1, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 5, 4, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 1, 2, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 3, 1, 2, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 5, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 1, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 5, 4, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 3, 1, 2, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}] , [[5, 4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 127, 408, 1346, 4533, 15518, 53837, 188864, 668802, 2387503, 8582691, 31042653, 112885776, 412482587, 1513699914, 5576428245] "" "Class ", 4965, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 1, 2, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 5, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 5, 4, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 1, 2, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 3, 1, 2, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 5, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 5, 4, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 3, 1, 2, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1211, 3875, 12548, 41040, 135370, 449791, 1504057, 5057668, 17092030, 58018150, 197727023, 676290905, 2320721255] "" "Class ", 4966, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 1, 2, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 5, 3, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 1, 3, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 5, 4, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 1, 2, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 4, 5, 3, 2], [0, 1, 0, 0]]} "Class ", 4967, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 1, 2, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 5, 3, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 1, 3, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 5, 4, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 1, 2, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 4, 5, 3, 2], [1, 1, 0, 0]]} "Class ", 4968, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 1, 2, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 5, 3, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 1, 3, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 5, 4, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 1, 2, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 4, 5, 3, 2], [0, 0, 1, 0]]} "Class ", 4969, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 1, 2, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 5, 3, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 1, 3, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 5, 4, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 1, 2, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 4, 5, 3, 2], [1, 0, 1, 0]]} "Class ", 4970, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 1, 2, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 5, 3, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 1, 3, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 5, 4, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 1, 2, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 4, 5, 3, 2], [0, 1, 1, 0]]} "Class ", 4971, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 1, 2, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 5, 3, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 1, 3, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 5, 4, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 1, 2, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 4, 5, 3, 2], [1, 1, 1, 0]]} "Class ", 4972, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 1, 2, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 5, 3, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 1, 3, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 5, 4, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 1, 2, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 4, 5, 3, 2], [0, 0, 0, 1]]} "Class ", 4973, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 1, 2, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 5, 4, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 1, 2, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]} "Class ", 4974, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 1, 2, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 5, 3, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 1, 3, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 5, 4, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 1, 2, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 4, 5, 3, 2], [0, 1, 0, 1]]} "Class ", 4975, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 1, 2, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 5, 3, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 1, 3, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 5, 4, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 1, 2, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 4, 5, 3, 2], [1, 1, 0, 1]]} "Class ", 4976, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 1, 2, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 5, 3, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 1, 3, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 5, 4, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 1, 2, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 4, 5, 3, 2], [0, 0, 1, 1]]} "Class ", 4977, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 1, 2, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 5, 3, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 1, 3, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 5, 4, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 1, 2, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 4, 5, 3, 2], [1, 0, 1, 1]]} "Class ", 4978, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 1, 2, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 5, 3, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 1, 3, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 5, 4, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 1, 2, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 4, 5, 3, 2], [0, 1, 1, 1]]} "Class ", 4979, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 1, 2, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 4, 5, 3, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 2, 1, 3, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 5, 4, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 1, 2, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[1, 4, 5, 3, 2], [1, 1, 1, 1]]} "Class ", 4980, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 1, 5, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 5, 3, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 1, 3, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 5, 1, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 1, 5, 2], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 1, 5, 3, 2], [0, 1, 0, 0]]} "Class ", 4981, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 1, 5, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 5, 3, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 1, 3, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 5, 1, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 1, 5, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 1, 5, 3, 2], [1, 1, 0, 0]]} "Class ", 4982, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 1, 5, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 5, 3, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 1, 3, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 5, 1, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 1, 5, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 1, 5, 3, 2], [0, 1, 1, 0]]} "Class ", 4983, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 1, 5, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 5, 3, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 1, 3, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 5, 1, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 1, 5, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 1, 5, 3, 2], [1, 1, 1, 0]]} "Class ", 4984, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 1, 5, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 5, 3, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 1, 3, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 5, 1, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 1, 5, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 1, 5, 3, 2], [0, 1, 0, 1]]} "Class ", 4985, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 1, 5, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 5, 3, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 1, 3, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 5, 1, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 1, 5, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 1, 5, 3, 2], [1, 1, 0, 1]]} "Class ", 4986, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 1, 5, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 5, 3, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 1, 3, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 5, 1, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 1, 5, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 1, 5, 3, 2], [0, 1, 1, 1]]} "Class ", 4987, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 1, 5, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 1, 5, 3, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 5, 1, 3, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 5, 1, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 1, 5, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 1, 5, 3, 2], [1, 1, 1, 1]]} "Class ", 4988, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [[4, 3, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}] , [[5, 4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {1, 2, 3, 4}, {[0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 127, 408, 1346, 4533, 15518, 53837, 188864, 668802, 2387503, 8582691, 31042653, 112885776, 412482587, 1513699914, 5576428245] "" "Class ", 4989, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1210, 3865, 12482, 40677, 133572, 441468, 1467296, 4900760, 16439370, 55357305, 187050302, 633998079, 2154950454] "" "Class ", 4990, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 3, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 3, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 5, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 4, 3, 2], [0, 1, 0, 0]]} "Class ", 4991, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 3, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 5, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 3, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 5, 1], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3, 5], {4, 5}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 3, 1, 2, 5], {3, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [ [5, 2, 1, 3, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 357, 1053, 3110, 9206, 27319, 81259, 242193, 723110, 2162162, 6473259, 19401540, 58206157, 174772167, 525176245] "" "Class ", 4992, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 3, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 3, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 5, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 4, 3, 2], [0, 0, 1, 0]]} "Class ", 4993, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 3, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 3, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 5, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 3, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 3, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 5, 1], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1033, 2986, 8594, 24674, 70757, 202814, 581272, 1666003, 4775323, 13688536, 39240095, 112490042, 322480613] "" "Class ", 4994, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 3, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 3, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 5, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 4, 3, 2], [0, 1, 1, 0]]} "Class ", 4995, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 3, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 3, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 5, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 3, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 3, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 5, 1], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 119, 336, 927, 2527, 6870, 18717, 51155, 140120, 384147, 1053147, 2886182, 7906953, 21657679, 59318944, 162475127] "" "Class ", 4996, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 5, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]} "Class ", 4997, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 5, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]} "Class ", 4998, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 3, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 3, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 5, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 4, 3, 2], [0, 1, 0, 1]]} "Class ", 4999, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 5, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 5, 1], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3, 5], {4, 5}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 3, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 120, 346, 984, 2775, 7797, 21889, 61474, 172757, 485727, 1366035, 3842119, 10806399, 30393424, 85480456, 240406851] "" "Class ", 5000, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 3, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 3, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 5, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 4, 3, 2], [0, 0, 1, 1]]} "Class ", 5001, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 3, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 3, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 5, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[1, 5, 4, 3, 2], [1, 0, 1, 1]]} "Class ", 5002, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 3, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 3, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 5, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[1, 5, 4, 3, 2], [0, 1, 1, 1]]} "Class ", 5003, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 5, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 5, 1], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 119, 336, 927, 2527, 6870, 18717, 51155, 140120, 384147, 1053147, 2886182, 7906953, 21657679, 59318944, 162475127] "" "Class ", 5004, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 4, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 2, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 1, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 4, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 2, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 1, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [ [3, 2, 1, 4, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 401, 1311, 4376, 14850, 51077, 177660, 623833, 2208378, 7872910, 28240520, 101852500, 369122649, 1343536175, 4909309244] "" "Class ", 5005, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 4, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 2, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 1, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 4, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 2, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 1, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4158, 13873, 46893, 160247, 552723, 1921756, 6728347, 23701026, 83939765, 298712615, 1067598164, 3830414563] "" "Class ", 5006, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 5, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 4, 3, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 2, 3, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 1, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 2, 5, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 4, 3, 2], [0, 1, 0, 0]]} "Class ", 5007, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 5, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 4, 3, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 2, 3, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 1, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 2, 5, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 4, 3, 2], [1, 1, 0, 0]]} "Class ", 5008, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 5, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 4, 3, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 2, 3, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 1, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 2, 5, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 4, 3, 2], [0, 0, 1, 0]]} "Class ", 5009, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 5, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 4, 3, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 2, 3, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 1, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 2, 5, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 4, 3, 2], [1, 0, 1, 0]]} "Class ", 5010, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 5, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 4, 3, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 2, 3, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 1, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 2, 5, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 4, 3, 2], [0, 1, 1, 0]]} "Class ", 5011, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 5, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 4, 3, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 2, 3, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 1, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 2, 5, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 4, 3, 2], [1, 1, 1, 0]]} "Class ", 5012, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 5, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 4, 3, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 2, 3, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 1, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 2, 5, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 4, 3, 2], [0, 0, 0, 1]]} "Class ", 5013, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 5, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 4, 3, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 2, 3, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 1, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 2, 5, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 4, 3, 2], [1, 0, 0, 1]]} "Class ", 5014, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 5, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 4, 3, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 2, 3, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 1, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 2, 5, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 4, 3, 2], [0, 1, 0, 1]]} "Class ", 5015, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 5, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 4, 3, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 2, 3, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 1, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 2, 5, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 4, 3, 2], [1, 1, 0, 1]]} "Class ", 5016, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 5, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 4, 3, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 2, 3, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 1, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 2, 5, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 4, 3, 2], [0, 0, 1, 1]]} "Class ", 5017, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 5, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 4, 3, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 2, 3, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 1, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 2, 5, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 4, 3, 2], [1, 0, 1, 1]]} "Class ", 5018, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 5, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 4, 3, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 2, 3, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 1, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 2, 5, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 1, 4, 3, 2], [0, 1, 1, 1]]} "Class ", 5019, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 5, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 1, 4, 3, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 5, 2, 3, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 4, 1, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 2, 5, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 1, 4, 3, 2], [1, 1, 1, 1]]} "Class ", 5020, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 5, 4], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 5, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 401, 1310, 4369, 14814, 50913, 176958, 620929, 2196606, 7825793, 28053502, 101114369, 366220798, 1332159745, 4864798206] "" "Class ", 5021, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 5, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 5, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4158, 13873, 46893, 160247, 552723, 1921756, 6728347, 23701026, 83939765, 298712615, 1067598164, 3830414563] "" "Class ", 5022, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 5, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [0, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 5, 4], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [0, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 5023, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 3, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 3, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 5, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 3, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 3, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 5, 4], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 5024, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 3, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 3, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 5, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[4, 5, 1, 3, 2], [0, 0, 1, 0]]} "Class ", 5025, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 3, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 3, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 5, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[4, 5, 1, 3, 2], [1, 0, 1, 0]]} "Class ", 5026, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 3, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 3, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 5, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 5, 1, 3, 2], [0, 1, 1, 0]]} "Class ", 5027, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 3, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 3, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 5, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 5, 1, 3, 2], [1, 1, 1, 0]]} "Class ", 5028, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 3, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 5, 4], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]} "Class ", 5029, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 3, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 3, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 5, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[4, 5, 1, 3, 2], [1, 0, 0, 1]]} "Class ", 5030, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 5, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]} "Class ", 5031, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 3, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 3, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 5, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 5, 1, 3, 2], [1, 1, 0, 1]]} "Class ", 5032, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 3, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 3, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 5, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[4, 5, 1, 3, 2], [0, 0, 1, 1]]} "Class ", 5033, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 3, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 3, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 5, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[4, 5, 1, 3, 2], [1, 0, 1, 1]]} "Class ", 5034, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 3, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 3, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 5, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 5, 1, 3, 2], [0, 1, 1, 1]]} "Class ", 5035, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 1, 3, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 5, 3, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 5, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 5, 1, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 5, 1, 3, 2], [1, 1, 1, 1]]} "Class ", 5036, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}] , [[4, 3, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1267, 4166, 13918, 47109, 161205, 556783, 1938487, 6796031, 23971361, 85009671, 302918609, 1084049439, 3894514424] "" "Class ", 5037, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 377, 1179, 3754, 12139, 39769, 131737, 440521, 1485092, 5042054, 17224693, 59166043, 204224955, 708009769, 2464197596] "" "Class ", 5038, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 3, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [0, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 3, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [0, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 1, 2], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 5039, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 3, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 3, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 3, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 3, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}], [ [3, 2, 4, 1, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 1, 2], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 366, 1105, 3356, 10251, 31483, 97186, 301431, 939004, 2936896, 9219531, 29040111, 91757034, 290754383, 923769926] "" "Class ", 5040, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 3, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 3, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 4, 1, 3, 2], [0, 0, 1, 0]]} "Class ", 5041, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 3, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 3, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 4, 1, 3, 2], [1, 0, 1, 0]]} "Class ", 5042, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 3, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 3, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 4, 1, 3, 2], [0, 1, 1, 0]]} "Class ", 5043, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 3, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 3, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 4, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 4, 1, 3, 2], [1, 1, 1, 0]]} "Class ", 5044, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 3, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 4, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]} "Class ", 5045, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 3, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 4, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]} "Class ", 5046, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 3, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 4, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]} "Class ", 5047, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 3, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 4, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]} "Class ", 5048, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 3, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 3, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 4, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 4, 1, 3, 2], [0, 0, 1, 1]]} "Class ", 5049, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 3, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 3, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 4, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 4, 1, 3, 2], [1, 0, 1, 1]]} "Class ", 5050, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 3, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 4, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]} "Class ", 5051, " is:" {{[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 1, 3, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 5, 3, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 3, 1, 4, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 3, 5, 2, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 4, 1, 3, 2], [1, 1, 1, 1]]} "Class ", 5052, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 5, 4, 3], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 5, 4, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 401, 1311, 4376, 14850, 51077, 177660, 623833, 2208378, 7872910, 28240520, 101852500, 369122649, 1343536175, 4909309244] "" "Class ", 5053, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 5, 4, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 5, 4, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1267, 4167, 13928, 47175, 161563, 558527, 1946444, 6830829, 24119213, 85625143, 305442436, 1094281935, 3935638646] "" "Class ", 5054, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 1, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 5, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 5, 4, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 4, 5, 1, 2], [0, 1, 0, 0]]} "Class ", 5055, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 1, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 5, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 5, 4, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[3, 4, 5, 1, 2], [1, 1, 0, 0]]} "Class ", 5056, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 5057, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 5058, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 1, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 5, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 1, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 5, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 5059, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 1, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 5, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 1, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 5, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 5060, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 5, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 5, 4, 3], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]} "Class ", 5061, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 1, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 5, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 5, 4, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[3, 4, 5, 1, 2], [1, 0, 0, 1]]} "Class ", 5062, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 1, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 5, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 5, 4, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 4, 5, 1, 2], [0, 1, 0, 1]]} "Class ", 5063, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 1, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 5, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 5, 4, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[3, 4, 5, 1, 2], [1, 1, 0, 1]]} "Class ", 5064, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 1, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 5, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[3, 4, 5, 1, 2], [0, 0, 1, 1]]} "Class ", 5065, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 5, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 1]]} "Class ", 5066, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 1, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 5, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 4, 5, 1, 2], [0, 1, 1, 1]]} "Class ", 5067, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 1, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 5, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[3, 4, 5, 1, 2], [1, 1, 1, 1]]} "Class ", 5068, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 1, 3, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 5, 1, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 1, 5, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 5, 3, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 1, 3, 2], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 3, 5, 1, 2], [0, 1, 0, 0]]} "Class ", 5069, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 1, 3, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 5, 1, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 1, 5, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 5, 3, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 1, 3, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 3, 5, 1, 2], [1, 1, 0, 0]]} "Class ", 5070, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 5, 1, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 1, 5, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 5, 1, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 1, 5, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 5071, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 5, 1, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 1, 5, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 5, 1, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 1, 5, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 5072, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 1, 3, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 5, 1, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 1, 5, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 5, 3, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 1, 3, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 3, 5, 1, 2], [0, 1, 0, 1]]} "Class ", 5073, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 1, 3, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 5, 1, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 1, 5, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 5, 3, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 1, 3, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 3, 5, 1, 2], [1, 1, 0, 1]]} "Class ", 5074, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 5, 1, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 1, 5, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 3, 5, 1, 2], [0, 1, 1, 1]]} "Class ", 5075, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 5, 1, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 1, 5, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 3, 5, 1, 2], [1, 1, 1, 1]]} "Class ", 5076, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 5, 3], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 5, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1, 5], {1, 2, 3}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 401, 1311, 4376, 14850, 51077, 177660, 623833, 2208378, 7872910, 28240520, 101852500, 369122649, 1343536175, 4909309244] "" "Class ", 5077, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 5, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 5, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1211, 3875, 12548, 41040, 135370, 449791, 1504057, 5057668, 17092030, 58018150, 197727023, 676290905, 2320721255] "" "Class ", 5078, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 1, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 5, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 5, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 5, 4, 1, 2], [0, 1, 0, 0]]} "Class ", 5079, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 1, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 5, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 5, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 1, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 5, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 5, 3], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [ [3, 4, 1, 2, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1158, 3615, 11393, 36209, 115940, 373709, 1211740, 3949969, 12937612, 42558745, 140547051, 465799527, 1548766044] "" "Class ", 5080, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1, 5], {1, 2, 3}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 5081, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 5082, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 1, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 5, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 5, 4, 1, 2], [0, 1, 1, 0]]} "Class ", 5083, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 1, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 5, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 1, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 5, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 5084, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 1, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 5, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 5, 3], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[3, 5, 4, 1, 2], [0, 0, 0, 1]]} "Class ", 5085, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 1, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 5, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 5, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[3, 5, 4, 1, 2], [1, 0, 0, 1]]} "Class ", 5086, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 1, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 5, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 5, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 5, 4, 1, 2], [0, 1, 0, 1]]} "Class ", 5087, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 1, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 5, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 5, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[3, 5, 4, 1, 2], [1, 1, 0, 1]]} "Class ", 5088, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 1, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 5, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[3, 5, 4, 1, 2], [0, 0, 1, 1]]} "Class ", 5089, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 1, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 5, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[3, 5, 4, 1, 2], [1, 0, 1, 1]]} "Class ", 5090, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 1, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 5, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 5, 4, 1, 2], [0, 1, 1, 1]]} "Class ", 5091, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 1, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 5, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 2, 1, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[3, 5, 4, 1, 2], [1, 1, 1, 1]]} "Class ", 5092, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 3, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 3, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 394, 1273, 4194, 14039, 47614, 163266, 565072, 1971476, 6926313, 24482914, 87009495, 310710172, 1114326403, 4011922558] "" "Class ", 5093, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 3, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 3, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 377, 1180, 3763, 12189, 39994, 132647, 444000, 1497995, 5089109, 17394637, 59776318, 206409201, 715813258, 2492053352] "" "Class ", 5094, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 1, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 5, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 3, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 3, 4, 1, 2], [0, 1, 0, 0]]} "Class ", 5095, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 1, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 5, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 3, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 3, 4, 1, 2], [1, 1, 0, 0]]} "Class ", 5096, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 5097, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 354, 1021, 2901, 8130, 22513, 61713, 167746, 452789, 1215197, 3246050, 8637641, 22912633, 60624546, 160075117] "" "Class ", 5098, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 1, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 5, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 3, 4, 1, 2], [0, 1, 1, 0]]} "Class ", 5099, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 1, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 5, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 3, 4, 1, 2], [1, 1, 1, 0]]} "Class ", 5100, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 5, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 3, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]} "Class ", 5101, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 5, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 3, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]} "Class ", 5102, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 1, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 5, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 3, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 3, 4, 1, 2], [0, 1, 0, 1]]} "Class ", 5103, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 1, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 5, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 3, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 3, 4, 1, 2], [1, 1, 0, 1]]} "Class ", 5104, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 5, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]} "Class ", 5105, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]} "Class ", 5106, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 1, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 5, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 3, 4, 1, 2], [0, 1, 1, 1]]} "Class ", 5107, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 1, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 5, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 3, 4, 1, 2], [1, 1, 1, 1]]} "Class ", 5108, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 5, 4], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 5, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1, 5], {1, 2, 3}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4159, 13883, 46959, 160608, 554500, 1929947, 6764488, 23855708, 84587419, 301380544, 1078453368, 3874161462] "" "Class ", 5109, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 5, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 5, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1211, 3875, 12548, 41040, 135370, 449791, 1504057, 5057668, 17092030, 58018150, 197727023, 676290905, 2320721255] "" "Class ", 5110, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 5, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 5, 4], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1, 5], {3, 5}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {4}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 354, 1021, 2901, 8130, 22513, 61713, 167746, 452789, 1215197, 3246050, 8637641, 22912633, 60624546, 160075117] "" "Class ", 5111, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 1, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 5, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 5, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 1, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 5, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 5, 4], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 354, 1021, 2901, 8130, 22513, 61713, 167746, 452789, 1215197, 3246050, 8637641, 22912633, 60624546, 160075117] "" "Class ", 5112, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 5, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 5, 4], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1, 5], {1, 2, 3}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 5113, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 5114, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 5, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 5, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 5, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 5, 4], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1, 5], {3, 5}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {4}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 354, 1021, 2901, 8130, 22513, 61713, 167746, 452789, 1215197, 3246050, 8637641, 22912633, 60624546, 160075117] "" "Class ", 5115, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 1, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 5, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 5, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 1, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 5, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 5, 4], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 354, 1021, 2901, 8130, 22513, 61713, 167746, 452789, 1215197, 3246050, 8637641, 22912633, 60624546, 160075117] "" "Class ", 5116, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 5, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 5, 4], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]} "Class ", 5117, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 1, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 5, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 5, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[4, 5, 3, 1, 2], [1, 0, 0, 1]]} "Class ", 5118, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 5, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]} "Class ", 5119, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 1, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 5, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 5, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 5, 3, 1, 2], [1, 1, 0, 1]]} "Class ", 5120, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 5, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 5, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]} "Class ", 5121, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 5, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 5, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 1]]} "Class ", 5122, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 5, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 5, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]} "Class ", 5123, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 1, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 5, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 5, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 3, 1, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 5, 3, 1, 2], [1, 1, 1, 1]]} "Class ", 5124, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1, 5], {1, 2, 3}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1210, 3865, 12482, 40677, 133572, 441468, 1467296, 4900760, 16439370, 55357305, 187050302, 633998079, 2154950454] "" "Class ", 5125, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 356, 1042, 3037, 8827, 25618, 74315, 215632, 626120, 1819845, 5295578, 15428589, 45006923, 131450682, 384376649] "" "Class ", 5126, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1, 5], {3, 5}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {4}, {[0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 354, 1021, 2901, 8130, 22513, 61713, 167746, 452789, 1215197, 3246050, 8637641, 22912633, 60624546, 160075117] "" "Class ", 5127, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 1, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 5, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 1, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 5, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[3, 4, 2, 1, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {4}, {[0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 119, 334, 902, 2351, 5945, 14660, 35408, 84061, 196715, 454778, 1040522, 2359451, 5308589, 11862208, 26345684] "" "Class ", 5128, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1, 5], {1, 2, 3}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 5129, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 120, 345, 972, 2691, 7348, 19855, 53230, 141871, 376466, 995705, 2627018, 6918101, 18192804, 47791365, 125443416] "" "Class ", 5130, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 5, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 5, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1, 5], {3, 5}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {4}, {[0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 354, 1021, 2901, 8130, 22513, 61713, 167746, 452789, 1215197, 3246050, 8637641, 22912633, 60624546, 160075117] "" "Class ", 5131, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 5, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 5, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 4, 5], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[3, 4, 2, 1, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {4}, {[0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 119, 334, 902, 2351, 5945, 14660, 35408, 84061, 196715, 454778, 1040522, 2359451, 5308589, 11862208, 26345684] "" "Class ", 5132, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 4, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]} "Class ", 5133, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 4, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]} "Class ", 5134, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 4, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]} "Class ", 5135, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 5, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 4, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]} "Class ", 5136, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 5, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 4, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]} "Class ", 5137, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 5, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 4, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]} "Class ", 5138, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 5, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 4, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 1, 1]]} "Class ", 5139, " is:" {{[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 5, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[2, 1, 3, 4, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[4, 5, 3, 2, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]} "Class ", 5140, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 1, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 127, 408, 1346, 4533, 15518, 53837, 188864, 668802, 2387503, 8582691, 31042653, 112885776, 412482587, 1513699914, 5576428245] "" "Class ", 5141, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [4, 1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 401, 1310, 4369, 14814, 50913, 176958, 620929, 2196606, 7825793, 28053502, 101114369, 366220798, 1332159745, 4864798206] "" "Class ", 5142, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 5, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 4, 3, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 3, 4, 5, 1], [0, 1, 0, 0]]} "Class ", 5143, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 5, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 4, 3, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 3, 4, 5, 1], [1, 1, 0, 0]]} "Class ", 5144, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 4, 3, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 1, 0]]} "Class ", 5145, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 4, 3, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 1, 0]]} "Class ", 5146, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 5, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 4, 3, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 3, 4, 5, 1], [0, 1, 1, 0]]} "Class ", 5147, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 5, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 4, 3, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 3, 4, 5, 1], [1, 1, 1, 0]]} "Class ", 5148, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1210, 3865, 12482, 40677, 133572, 441468, 1467296, 4900760, 16439370, 55357305, 187050302, 633998079, 2154950454] "" "Class ", 5149, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [4, 1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 5150, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 5, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 5, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {2}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 5151, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 5, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 5, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [4, 1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 5152, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1210, 3865, 12482, 40677, 133572, 441468, 1467296, 4900760, 16439370, 55357305, 187050302, 633998079, 2154950454] "" "Class ", 5153, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [4, 1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 5154, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 5, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 5, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {2}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 5155, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 5, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 4, 5, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [4, 1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 5156, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 2, 4, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 4, 5, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 2, 1, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 4, 2, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 2, 4, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 2, 4, 5, 1], [0, 1, 0, 0]]} "Class ", 5157, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 2, 4, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 4, 5, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 2, 1, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 4, 2, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 2, 4, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[3, 2, 4, 5, 1], [1, 1, 0, 0]]} "Class ", 5158, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 2, 4, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 4, 5, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 2, 1, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 4, 2, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 2, 4, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 2, 4, 5, 1], [0, 1, 1, 0]]} "Class ", 5159, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 2, 4, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 4, 5, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 2, 1, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 4, 2, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 2, 4, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[3, 2, 4, 5, 1], [1, 1, 1, 0]]} "Class ", 5160, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 4, 5, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 2, 1, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 4, 5, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 2, 1, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 5161, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 4, 5, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 2, 1, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 4, 5, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 2, 1, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 5162, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 4, 5, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 2, 1, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 4, 5, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 2, 1, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 5163, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 4, 5, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 2, 1, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 4, 5, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 2, 1, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 5164, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 3, 2, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 3, 5, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 3, 1, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 3, 4, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 3, 2, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[2, 4, 3, 5, 1], [0, 0, 1, 0]]} "Class ", 5165, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 3, 2, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 3, 5, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 3, 1, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 3, 4, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 3, 2, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[2, 4, 3, 5, 1], [1, 0, 1, 0]]} "Class ", 5166, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 3, 2, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 3, 5, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 3, 1, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 3, 4, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 3, 2, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 4, 3, 5, 1], [0, 1, 1, 0]]} "Class ", 5167, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 3, 2, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 3, 5, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 3, 1, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 3, 4, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 3, 2, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 4, 3, 5, 1], [1, 1, 1, 0]]} "Class ", 5168, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 3, 5, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 3, 1, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 3, 5, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 3, 1, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 5169, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 3, 5, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 3, 1, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 3, 5, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 3, 1, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 5170, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 3, 5, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 3, 1, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 3, 5, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 3, 1, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 5171, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 3, 5, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 3, 1, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 3, 5, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 3, 1, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 5172, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 3, 4, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 3, 5, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 3, 1, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 3, 2, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 3, 4, 2], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[4, 2, 3, 5, 1], [0, 0, 1, 0]]} "Class ", 5173, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 3, 4, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 3, 5, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 3, 1, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 3, 2, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 3, 4, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[4, 2, 3, 5, 1], [1, 0, 1, 0]]} "Class ", 5174, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 3, 4, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 3, 5, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 3, 1, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 3, 2, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 3, 4, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 2, 3, 5, 1], [0, 1, 1, 0]]} "Class ", 5175, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 3, 4, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 3, 5, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 3, 1, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 3, 2, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 3, 4, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 2, 3, 5, 1], [1, 1, 1, 0]]} "Class ", 5176, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 3, 5, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 3, 1, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 3, 5, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 3, 1, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 5177, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 3, 5, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 3, 1, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 3, 5, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 3, 1, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 5178, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 3, 5, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 3, 1, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 3, 5, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 3, 1, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 5179, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 3, 5, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 3, 1, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 3, 5, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 3, 1, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 5180, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 4, 2, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 2, 4, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 4, 2, 3], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 1, 0]]} "Class ", 5181, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 4, 2, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 4, 1, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 2, 4, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 4, 2, 3], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 0]]} "Class ", 5182, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 4, 2, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 2, 5, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 4, 1, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 2, 4, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 4, 2, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 4, 2, 5, 1], [0, 1, 1, 0]]} "Class ", 5183, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 4, 2, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 4, 1, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 2, 4, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 4, 2, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 0]]} "Class ", 5184, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 5185, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 4, 1, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 4, 1, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 5186, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 2, 5, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 4, 1, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 2, 5, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 4, 1, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 5187, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 4, 1, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 4, 1, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 5188, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 4, 3, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 2, 5, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 4, 1, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 2, 3, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 4, 3, 2], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[4, 3, 2, 5, 1], [0, 0, 1, 0]]} "Class ", 5189, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 4, 3, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 2, 5, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 4, 1, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 2, 3, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 4, 3, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[4, 3, 2, 5, 1], [1, 0, 1, 0]]} "Class ", 5190, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 4, 3, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 2, 5, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 4, 1, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 2, 3, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 4, 3, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 3, 2, 5, 1], [0, 1, 1, 0]]} "Class ", 5191, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 4, 3, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 2, 5, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 4, 1, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 2, 3, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 4, 3, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 3, 2, 5, 1], [1, 1, 1, 0]]} "Class ", 5192, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 2, 5, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 4, 1, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 2, 5, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 4, 1, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 5193, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 2, 5, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 4, 1, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 2, 5, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 4, 1, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 5194, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 2, 5, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 4, 1, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 2, 5, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 4, 1, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 5195, " is:" {{[[1, 3, 2], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 2, 5, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 4, 1, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 2, 5, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 4, 1, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 5196, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 5, 4, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 1, 2, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 5, 3, 2], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 5, 4, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 1, 2, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 5, 3, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [ [4, 2, 1, 3, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 127, 408, 1346, 4533, 15518, 53837, 188864, 668802, 2387503, 8582691, 31042653, 112885776, 412482587, 1513699914, 5576428245] "" "Class ", 5197, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 5, 4, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 1, 2, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 5, 3, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 5, 4, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 1, 2, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 5, 3, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [4, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 401, 1310, 4369, 14814, 50913, 176958, 620929, 2196606, 7825793, 28053502, 101114369, 366220798, 1332159745, 4864798206] "" "Class ", 5198, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 5, 4, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 1, 2, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 5, 3, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 3, 5, 4, 1], [0, 1, 0, 0]]} "Class ", 5199, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 5, 4, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 1, 2, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 5, 3, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 3, 5, 4, 1], [1, 1, 0, 0]]} "Class ", 5200, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 5, 4, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 1, 2, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 5, 3, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[2, 3, 5, 4, 1], [0, 0, 1, 0]]} "Class ", 5201, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 5, 4, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 1, 2, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 5, 3, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[2, 3, 5, 4, 1], [1, 0, 1, 0]]} "Class ", 5202, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 5, 4, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 1, 2, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 5, 3, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 3, 5, 4, 1], [0, 1, 1, 0]]} "Class ", 5203, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 5, 4, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 1, 2, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 5, 3, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 3, 5, 4, 1], [1, 1, 1, 0]]} "Class ", 5204, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 5, 4, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 1, 2, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 5, 4, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 1, 2, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}], [ [4, 2, 1, 3, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1211, 3875, 12548, 41040, 135370, 449791, 1504057, 5057668, 17092030, 58018150, 197727023, 676290905, 2320721255] "" "Class ", 5205, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 5, 4, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 1, 2, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 5, 4, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 1, 2, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [4, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 5206, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 5, 4, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 1, 2, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 5, 4, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 1, 2, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}], [ [4, 2, 1, 3, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 5207, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 5, 4, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 1, 2, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 5, 4, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 1, 2, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [4, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 5208, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 5, 4, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 1, 2, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[2, 3, 5, 4, 1], [0, 0, 1, 1]]} "Class ", 5209, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 5, 4, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 1, 2, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[2, 3, 5, 4, 1], [1, 0, 1, 1]]} "Class ", 5210, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 5, 4, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 1, 2, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 5, 4, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 1, 2, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}], [ [4, 2, 1, 3, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 5211, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 5, 4, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 1, 2, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 5, 4, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 3, 1, 2, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [4, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 5212, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 1, 4, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 5, 4, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 1, 2, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 5, 2, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 1, 4, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 2, 5, 4, 1], [0, 1, 0, 0]]} "Class ", 5213, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 1, 4, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 5, 4, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 1, 2, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 5, 2, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 1, 4, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[3, 2, 5, 4, 1], [1, 1, 0, 0]]} "Class ", 5214, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 1, 4, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 5, 4, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 1, 2, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 5, 2, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 1, 4, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 2, 5, 4, 1], [0, 1, 1, 0]]} "Class ", 5215, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 1, 4, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 5, 4, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 1, 2, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 5, 2, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 1, 4, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[3, 2, 5, 4, 1], [1, 1, 1, 0]]} "Class ", 5216, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 5, 4, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 1, 2, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 5, 4, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 1, 2, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 5217, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 5, 4, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 1, 2, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 5, 4, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 1, 2, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 5218, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 5, 4, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 1, 2, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 5, 4, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 1, 2, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 5219, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 5, 4, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 1, 2, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 5, 4, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 4, 1, 2, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 5220, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 3, 4, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 3, 2, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 5, 2], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 3, 4, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 3, 2, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 5, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 127, 408, 1346, 4533, 15518, 53837, 188864, 668802, 2387503, 8582691, 31042653, 112885776, 412482587, 1513699914, 5576428245] "" "Class ", 5221, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 3, 4, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 3, 2, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 5, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 3, 4, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 3, 2, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 5, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4158, 13873, 46893, 160247, 552723, 1921756, 6728347, 23701026, 83939765, 298712615, 1067598164, 3830414563] "" "Class ", 5222, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 3, 4, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 3, 2, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 5, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 5, 3, 4, 1], [0, 1, 0, 0]]} "Class ", 5223, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 3, 4, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 3, 2, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 5, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 3, 4, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 3, 2, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 5, 2], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1222, 3951, 12974, 43163, 145198, 493089, 1688266, 5821647, 20200416, 70480443, 247119160, 870262599, 3076876534] "" "Class ", 5224, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 3, 4, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 3, 2, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 5, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[2, 5, 3, 4, 1], [0, 0, 1, 0]]} "Class ", 5225, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 3, 4, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 3, 2, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 5, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[2, 5, 3, 4, 1], [1, 0, 1, 0]]} "Class ", 5226, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 3, 4, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 3, 2, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 5, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 5, 3, 4, 1], [0, 1, 1, 0]]} "Class ", 5227, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 3, 4, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 3, 2, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 5, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 5, 3, 4, 1], [1, 1, 1, 0]]} "Class ", 5228, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 3, 4, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 3, 2, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 3, 4, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 3, 2, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {2, 3, 4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1220, 3929, 12822, 42309, 140922, 473169, 1599864, 5442561, 18615176, 63975857, 220816906, 765121477, 2660426630] "" "Class ", 5229, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 3, 4, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 3, 2, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 3, 4, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 3, 2, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 5230, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 3, 4, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 3, 2, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 5, 3, 4, 1], [0, 1, 0, 1]]} "Class ", 5231, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 3, 4, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 3, 2, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 3, 4, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 3, 2, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 5232, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 3, 4, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 3, 2, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[2, 5, 3, 4, 1], [0, 0, 1, 1]]} "Class ", 5233, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 3, 4, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 3, 2, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[2, 5, 3, 4, 1], [1, 0, 1, 1]]} "Class ", 5234, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 3, 4, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 3, 2, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 5, 3, 4, 1], [0, 1, 1, 1]]} "Class ", 5235, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 3, 4, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 3, 2, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 3, 1, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 5, 3, 4, 1], [1, 1, 1, 1]]} "Class ", 5236, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 3, 4, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 3, 2, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 2, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 3, 4, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 3, 2, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 2, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 1, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 401, 1311, 4375, 14842, 51032, 177443, 622863, 2204225, 7855594, 28169565, 101565203, 367969229, 1338934195, 4891033042] "" "Class ", 5237, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 3, 4, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 3, 2, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 2, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 3, 4, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 3, 2, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 2, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [4, 1, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 386, 1232, 4016, 13321, 44824, 152637, 525001, 1821233, 6364492, 22384264, 79171069, 281421171, 1004802960, 3601987092] "" "Class ", 5238, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 3, 4, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 3, 2, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 2, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 2, 3, 4, 1], [0, 1, 0, 0]]} "Class ", 5239, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 3, 4, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 3, 2, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 2, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 2, 3, 4, 1], [1, 1, 0, 0]]} "Class ", 5240, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 3, 4, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 3, 2, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 2, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 2, 3, 4, 1], [0, 0, 1, 0]]} "Class ", 5241, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 3, 4, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 3, 2, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 2, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 2, 3, 4, 1], [1, 0, 1, 0]]} "Class ", 5242, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 3, 4, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 3, 2, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 2, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 2, 3, 4, 1], [0, 1, 1, 0]]} "Class ", 5243, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 3, 4, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 3, 2, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 2, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 2, 3, 4, 1], [1, 1, 1, 0]]} "Class ", 5244, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 3, 4, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 3, 2, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 3, 4, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 3, 2, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 5245, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 3, 4, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 3, 4, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}] , [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 5246, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 3, 4, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 3, 2, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 2, 3, 4, 1], [0, 1, 0, 1]]} "Class ", 5247, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 3, 4, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 3, 2, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 2, 3, 4, 1], [1, 1, 0, 1]]} "Class ", 5248, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 3, 4, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 3, 2, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 2, 3, 4, 1], [0, 0, 1, 1]]} "Class ", 5249, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 3, 4, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 3, 2, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 2, 3, 4, 1], [1, 0, 1, 1]]} "Class ", 5250, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 3, 4, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 3, 2, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 2, 3, 4, 1], [0, 1, 1, 1]]} "Class ", 5251, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 3, 4, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 3, 2, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 3, 4, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 2, 3, 4, 1], [1, 1, 1, 1]]} "Class ", 5252, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 4, 1, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 2, 4, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 4, 2, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 2, 5, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 4, 1, 3], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[3, 5, 2, 4, 1], [0, 0, 1, 0]]} "Class ", 5253, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 4, 1, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 2, 4, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 4, 2, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 2, 5, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 4, 1, 3], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[3, 5, 2, 4, 1], [1, 0, 1, 0]]} "Class ", 5254, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 4, 1, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 2, 4, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 4, 2, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 2, 5, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 4, 1, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 5, 2, 4, 1], [0, 1, 1, 0]]} "Class ", 5255, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 4, 1, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 2, 4, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 4, 2, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 2, 5, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 4, 1, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[3, 5, 2, 4, 1], [1, 1, 1, 0]]} "Class ", 5256, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 4, 1, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 2, 4, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 4, 2, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 2, 5, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 4, 1, 3], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[3, 5, 2, 4, 1], [0, 0, 1, 1]]} "Class ", 5257, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 4, 1, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 2, 4, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 4, 2, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 2, 5, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 4, 1, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[3, 5, 2, 4, 1], [1, 0, 1, 1]]} "Class ", 5258, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 4, 1, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 2, 4, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 4, 2, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 2, 5, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 4, 1, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 5, 2, 4, 1], [0, 1, 1, 1]]} "Class ", 5259, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 4, 1, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 2, 4, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 4, 2, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 2, 5, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 4, 1, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[3, 5, 2, 4, 1], [1, 1, 1, 1]]} "Class ", 5260, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 4, 3, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 2, 4, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 4, 2, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 2, 3, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 4, 3, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 3, 2, 4, 1], [0, 0, 1, 0]]} "Class ", 5261, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 4, 3, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 2, 4, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 4, 2, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 2, 3, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 4, 3, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 3, 2, 4, 1], [1, 0, 1, 0]]} "Class ", 5262, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 4, 3, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 2, 4, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 4, 2, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 2, 3, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 4, 3, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 3, 2, 4, 1], [0, 1, 1, 0]]} "Class ", 5263, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 4, 3, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 2, 4, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 4, 2, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 2, 3, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 4, 3, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 3, 2, 4, 1], [1, 1, 1, 0]]} "Class ", 5264, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 4, 3, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 2, 4, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 4, 2, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 4, 3, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 3, 2, 4, 1], [0, 0, 1, 1]]} "Class ", 5265, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 4, 3, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 2, 4, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 4, 2, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 4, 3, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 3, 2, 4, 1], [1, 0, 1, 1]]} "Class ", 5266, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 4, 3, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 2, 4, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 4, 2, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 4, 3, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 3, 2, 4, 1], [0, 1, 1, 1]]} "Class ", 5267, " is:" {{[[1, 3, 2], [0, 1]], [[5, 2, 4, 3, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 2, 4, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 4, 2, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 2, 4, 3, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 3, 2, 4, 1], [1, 1, 1, 1]]} "Class ", 5268, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 5, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 1, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 5, 4, 2], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 5, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 1, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 5, 4, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [ [4, 3, 1, 2, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 127, 408, 1346, 4533, 15518, 53837, 188864, 668802, 2387503, 8582691, 31042653, 112885776, 412482587, 1513699914, 5576428245] "" "Class ", 5269, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 5, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 1, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 5, 4, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 5, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 1, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 5, 4, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1265, 4149, 13818, 46608, 158898, 546685, 1895715, 6618905, 23249607, 82103555, 291322471, 1038099516, 3713430835] "" "Class ", 5270, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 5, 3, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 1, 3, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 5, 4, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 4, 5, 3, 1], [0, 1, 0, 0]]} "Class ", 5271, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 5, 3, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 1, 3, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 5, 4, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 4, 5, 3, 1], [1, 1, 0, 0]]} "Class ", 5272, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 5, 3, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 1, 3, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 5, 4, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[2, 4, 5, 3, 1], [0, 0, 1, 0]]} "Class ", 5273, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 5, 3, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 1, 3, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 5, 4, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[2, 4, 5, 3, 1], [1, 0, 1, 0]]} "Class ", 5274, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 5, 3, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 1, 3, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 5, 4, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 4, 5, 3, 1], [0, 1, 1, 0]]} "Class ", 5275, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 5, 3, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 1, 3, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 5, 4, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 4, 5, 3, 1], [1, 1, 1, 0]]} "Class ", 5276, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 5, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 1, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 5, 4, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 5, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 1, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 5, 4, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}], [ [4, 3, 1, 2, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {2, 3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4158, 13873, 46893, 160247, 552723, 1921756, 6728347, 23701026, 83939765, 298712615, 1067598164, 3830414563] "" "Class ", 5277, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 5, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 1, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 5, 4, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 5, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 1, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 5, 4, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 5278, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 5, 3, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 1, 3, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 5, 4, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 4, 5, 3, 1], [0, 1, 0, 1]]} "Class ", 5279, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 5, 3, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 1, 3, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 5, 4, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 4, 5, 3, 1], [1, 1, 0, 1]]} "Class ", 5280, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 5, 3, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 1, 3, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[2, 4, 5, 3, 1], [0, 0, 1, 1]]} "Class ", 5281, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 5, 3, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 1, 3, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[2, 4, 5, 3, 1], [1, 0, 1, 1]]} "Class ", 5282, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 5, 3, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 1, 3, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 4, 5, 3, 1], [0, 1, 1, 1]]} "Class ", 5283, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 4, 5, 3, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 2, 1, 3, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 1, 2, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[2, 4, 5, 3, 1], [1, 1, 1, 1]]} "Class ", 5284, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 1, 4, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 5, 3, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 1, 3, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 5, 2, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 1, 4, 2], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 2, 5, 3, 1], [0, 1, 0, 0]]} "Class ", 5285, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 1, 4, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 5, 3, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 1, 3, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 5, 2, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 1, 4, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 2, 5, 3, 1], [1, 1, 0, 0]]} "Class ", 5286, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 1, 4, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 5, 3, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 1, 3, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 5, 2, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 1, 4, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 2, 5, 3, 1], [0, 1, 1, 0]]} "Class ", 5287, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 1, 4, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 5, 3, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 1, 3, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 5, 2, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 1, 4, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 2, 5, 3, 1], [1, 1, 1, 0]]} "Class ", 5288, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 1, 4, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 5, 3, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 1, 3, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 5, 2, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 1, 4, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 2, 5, 3, 1], [0, 1, 0, 1]]} "Class ", 5289, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 1, 4, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 5, 3, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 1, 3, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 5, 2, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 1, 4, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 2, 5, 3, 1], [1, 1, 0, 1]]} "Class ", 5290, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 1, 4, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 5, 3, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 1, 3, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 1, 4, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 2, 5, 3, 1], [0, 1, 1, 1]]} "Class ", 5291, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 1, 4, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 2, 5, 3, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 4, 1, 3, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 1, 4, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 2, 5, 3, 1], [1, 1, 1, 1]]} "Class ", 5292, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 4, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 5, 2], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 4, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 5, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {1, 2, 3, 4}, {[0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 127, 408, 1346, 4533, 15518, 53837, 188864, 668802, 2387503, 8582691, 31042653, 112885776, 412482587, 1513699914, 5576428245] "" "Class ", 5293, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 4, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 4, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1221, 3939, 12886, 42648, 142544, 480459, 1631287, 5574073, 19153815, 66146259, 229452587, 799140681, 2793373937] "" "Class ", 5294, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 4, 3, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 5, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 5, 4, 3, 1], [0, 1, 0, 0]]} "Class ", 5295, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 4, 3, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 5, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 4, 3, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 5, 2], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 1, 0]}], [[4, 3, 1, 2, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {3, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 367, 1116, 3429, 10636, 33271, 104866, 332763, 1062330, 3409877, 10998602, 35632815, 115903574, 378372911, 1239314162] "" "Class ", 5296, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 4, 3, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 5, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[2, 5, 4, 3, 1], [0, 0, 1, 0]]} "Class ", 5297, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 4, 3, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 5, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 4, 3, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 5, 2], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 5298, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 4, 3, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 5, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 5, 4, 3, 1], [0, 1, 1, 0]]} "Class ", 5299, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 4, 3, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 5, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 4, 3, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 5, 2], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 356, 1044, 3057, 8948, 26192, 76674, 224465, 657137, 1923817, 5632105, 16488346, 48270655, 141315320, 413709331] "" "Class ", 5300, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 4, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 4, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {2, 3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {2, 3, 4}, {[0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4158, 13873, 46893, 160247, 552723, 1921756, 6728347, 23701026, 83939765, 298712615, 1067598164, 3830414563] "" "Class ", 5301, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 4, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 4, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 5302, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 4, 3, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 5, 4, 3, 1], [0, 1, 0, 1]]} "Class ", 5303, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 4, 3, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 4, 3, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 356, 1044, 3057, 8948, 26192, 76674, 224465, 657137, 1923817, 5632105, 16488346, 48270655, 141315320, 413709331] "" "Class ", 5304, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 4, 3, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[2, 5, 4, 3, 1], [0, 0, 1, 1]]} "Class ", 5305, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 4, 3, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 4, 3, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 5306, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 4, 3, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[2, 5, 4, 3, 1], [0, 1, 1, 1]]} "Class ", 5307, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 4, 3, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 5, 4, 3, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 356, 1044, 3057, 8948, 26192, 76674, 224465, 657137, 1923817, 5632105, 16488346, 48270655, 141315320, 413709331] "" "Class ", 5308, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 4, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 2, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 2, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 4, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 2, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 2, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [ [4, 2, 1, 3, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 401, 1311, 4375, 14842, 51032, 177443, 622863, 2204225, 7855594, 28169565, 101565203, 367969229, 1338934195, 4891033042] "" "Class ", 5309, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 4, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 2, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 2, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 4, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 2, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 2, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 386, 1232, 4016, 13321, 44824, 152637, 525001, 1821233, 6364492, 22384264, 79171069, 281421171, 1004802960, 3601987092] "" "Class ", 5310, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 4, 3, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 2, 3, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 2, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 2, 4, 3, 1], [0, 1, 0, 0]]} "Class ", 5311, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 4, 3, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 2, 3, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 2, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 2, 4, 3, 1], [1, 1, 0, 0]]} "Class ", 5312, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 4, 3, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 2, 3, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 2, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 2, 4, 3, 1], [0, 0, 1, 0]]} "Class ", 5313, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 4, 3, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 2, 3, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 2, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 2, 4, 3, 1], [1, 0, 1, 0]]} "Class ", 5314, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 4, 3, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 2, 3, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 2, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 2, 4, 3, 1], [0, 1, 1, 0]]} "Class ", 5315, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 4, 3, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 2, 3, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 2, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 2, 4, 3, 1], [1, 1, 1, 0]]} "Class ", 5316, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 4, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 2, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 4, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 2, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}], [ [4, 2, 1, 3, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 3, 4], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1221, 3939, 12885, 42636, 142456, 479944, 1628631, 5561411, 19096541, 65896618, 228393724, 794741412, 2775388162] "" "Class ", 5317, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 4, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 2, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 4, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 2, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}] , [[4, 3, 1, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 366, 1105, 3356, 10251, 31483, 97186, 301431, 939004, 2936896, 9219531, 29040111, 91757034, 290754383, 923769926] "" "Class ", 5318, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 4, 3, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 2, 3, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 2, 4, 3, 1], [0, 1, 0, 1]]} "Class ", 5319, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 4, 3, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 2, 3, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 2, 4, 3, 1], [1, 1, 0, 1]]} "Class ", 5320, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 4, 3, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 2, 3, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 2, 4, 3, 1], [0, 0, 1, 1]]} "Class ", 5321, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 4, 3, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 2, 3, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 2, 4, 3, 1], [1, 0, 1, 1]]} "Class ", 5322, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 4, 3, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 2, 3, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 2, 4, 3, 1], [0, 1, 1, 1]]} "Class ", 5323, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 2, 4, 3, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 4, 2, 3, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 2, 4, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 2, 4, 3, 1], [1, 1, 1, 1]]} "Class ", 5324, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 4, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 5, 4], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 4, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 5, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 402, 1317, 4403, 14963, 51537, 179503, 631144, 2237199, 7986056, 28683449, 103583004, 375874395, 1369853869, 5011826841] "" "Class ", 5325, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 2, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 4, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 5, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 2, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 4, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 5, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 394, 1273, 4193, 14029, 47551, 162935, 563487, 1964305, 6895072, 24350348, 86457606, 308445117, 1105131089, 3974909434] "" "Class ", 5326, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 5, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 5, 4], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {4, 5}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1095, 3294, 9943, 30136, 91754, 280693, 862816, 2664635, 8266165, 25751860, 80543830, 252844693, 796443768] "" "Class ", 5327, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 2, 3, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 4, 3, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 5, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 2, 3, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 4, 3, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 5, 4], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1095, 3294, 9943, 30136, 91754, 280693, 862816, 2664635, 8266165, 25751860, 80543830, 252844693, 796443768] "" "Class ", 5328, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 2, 3, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 4, 3, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 5, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[4, 5, 2, 3, 1], [0, 0, 1, 0]]} "Class ", 5329, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 2, 3, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 4, 3, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 5, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[4, 5, 2, 3, 1], [1, 0, 1, 0]]} "Class ", 5330, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 4, 3, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 5, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 1, 0]]} "Class ", 5331, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 2, 3, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 4, 3, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 5, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 5, 2, 3, 1], [1, 1, 1, 0]]} "Class ", 5332, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 4, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 4, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {2, 3, 4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1221, 3939, 12885, 42636, 142456, 479944, 1628631, 5561411, 19096541, 65896618, 228393724, 794741412, 2775388162] "" "Class ", 5333, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 2, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 4, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 2, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 4, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 5334, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {4, 5}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 354, 1021, 2901, 8130, 22513, 61713, 167746, 452789, 1215197, 3246050, 8637641, 22912633, 60624546, 160075117] "" "Class ", 5335, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 4, 3, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 4, 3, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 354, 1021, 2901, 8130, 22513, 61713, 167746, 452789, 1215197, 3246050, 8637641, 22912633, 60624546, 160075117] "" "Class ", 5336, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 2, 3, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 4, 3, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 5, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[4, 5, 2, 3, 1], [0, 0, 1, 1]]} "Class ", 5337, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 2, 3, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 4, 3, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 5, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[4, 5, 2, 3, 1], [1, 0, 1, 1]]} "Class ", 5338, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 4, 3, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 5, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]} "Class ", 5339, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 2, 3, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 4, 3, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 5, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 5, 2, 3, 1], [1, 1, 1, 1]]} "Class ", 5340, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 2, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 4, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 4, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 2, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 4, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 4, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4157, 13863, 46827, 159886, 550943, 1913526, 6691891, 23544320, 83280751, 295986327, 1056461081, 3785365874] "" "Class ", 5341, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 4, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 4, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 4, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 4, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3}, {[0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 369, 1138, 3577, 11434, 37077, 121694, 403537, 1349874, 4549601, 15434722, 52665073, 180616786, 622250597, 2152493550] "" "Class ", 5342, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 4, 3, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 4, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [0, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 4, 3, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 4, 5], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [0, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {4, 5}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {4}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1095, 3294, 9943, 30136, 91754, 280693, 862816, 2664635, 8266165, 25751860, 80543830, 252844693, 796443768] "" "Class ", 5343, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 2, 3, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 4, 3, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 4, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 2, 3, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 4, 3, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 4, 5], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4}, { [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {4}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 120, 347, 996, 2860, 8265, 24115, 71114, 211903, 637468, 1934027, 5911590, 18188070, 56281929, 175050672, 546926233] "" "Class ", 5344, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 2, 3, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 4, 3, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 4, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 4, 2, 3, 1], [0, 0, 1, 0]]} "Class ", 5345, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 2, 3, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 4, 3, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 4, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 4, 2, 3, 1], [1, 0, 1, 0]]} "Class ", 5346, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 4, 3, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 4, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 1, 0]]} "Class ", 5347, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 2, 3, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 4, 3, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 4, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 4, 2, 3, 1], [1, 1, 1, 0]]} "Class ", 5348, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 2, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 4, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 2, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 4, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 5349, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 4, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 4, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 120, 345, 972, 2691, 7348, 19855, 53230, 141871, 376466, 995705, 2627018, 6918101, 18192804, 47791365, 125443416] "" "Class ", 5350, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {4, 5}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {4}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 354, 1021, 2901, 8130, 22513, 61713, 167746, 452789, 1215197, 3246050, 8637641, 22912633, 60624546, 160075117] "" "Class ", 5351, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {2, 3, 4}, { [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {4}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 119, 334, 902, 2351, 5945, 14660, 35408, 84061, 196715, 454778, 1040522, 2359451, 5308589, 11862208, 26345684] "" "Class ", 5352, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 2, 3, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 4, 3, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 0]], [[5, 4, 2, 3, 1], [0, 0, 1, 1]]} "Class ", 5353, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 2, 3, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 4, 3, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 0]], [[5, 4, 2, 3, 1], [1, 0, 1, 1]]} "Class ", 5354, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 4, 3, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 1, 1]]} "Class ", 5355, " is:" {{[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 2, 3, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 4, 3, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 4, 2, 3, 1], [1, 1, 1, 1]]} "Class ", 5356, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 4, 3], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 4, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [ [4, 3, 1, 2, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 401, 1310, 4368, 14806, 50868, 176738, 619932, 2192288, 7807625, 27978530, 100809146, 364990184, 1327233335, 4845181810] "" "Class ", 5357, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 4, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 4, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1265, 4149, 13818, 46608, 158898, 546685, 1895715, 6618905, 23249607, 82103555, 291322471, 1038099516, 3713430835] "" "Class ", 5358, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 4, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 0, 0]]} "Class ", 5359, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 4, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 0, 0]]} "Class ", 5360, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [ [4, 3, 1, 2, 5], {1, 3, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 3, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {3, 4}, {[0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 5361, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1032, 2973, 8496, 24111, 68017, 190885, 533294, 1484021, 4115186, 11375765, 31358377, 86223943, 236540916] "" "Class ", 5362, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [ [4, 3, 1, 2, 5], {1, 3, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 3, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {3, 4}, {[0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 5363, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1032, 2973, 8496, 24111, 68017, 190885, 533294, 1484021, 4115186, 11375765, 31358377, 86223943, 236540916] "" "Class ", 5364, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}], [ [4, 3, 1, 2, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4158, 13873, 46893, 160247, 552723, 1921756, 6728347, 23701026, 83939765, 298712615, 1067598164, 3830414563] "" "Class ", 5365, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1212, 3885, 12614, 41400, 137132, 457841, 1539150, 5205612, 17700450, 60473476, 207491052, 714668954, 2470156910] "" "Class ", 5366, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 0, 1]]} "Class ", 5367, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 0, 1]]} "Class ", 5368, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 2, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 2, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [ [4, 3, 1, 2, 5], {1, 3, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {3, 4}, {[0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 5369, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1032, 2973, 8496, 24111, 68017, 190885, 533294, 1484021, 4115186, 11375765, 31358377, 86223943, 236540916] "" "Class ", 5370, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [ [4, 3, 1, 2, 5], {1, 3, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {3, 4}, {[0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 5371, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1032, 2973, 8496, 24111, 68017, 190885, 533294, 1484021, 4115186, 11375765, 31358377, 86223943, 236540916] "" "Class ", 5372, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 3, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 1, 4, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 3, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 1, 3, 2], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 0, 0]]} "Class ", 5373, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 3, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 5, 2, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 1, 4, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 3, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 1, 3, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 3, 5, 2, 1], [1, 1, 0, 0]]} "Class ", 5374, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 1, 4, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 1, 4, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 5375, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 5, 2, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 1, 4, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 5, 2, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 1, 4, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 5376, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 1, 4, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 3, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 0, 1]]} "Class ", 5377, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 5, 2, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 1, 4, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 3, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[4, 3, 5, 2, 1], [1, 1, 0, 1]]} "Class ", 5378, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 1, 4, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 1, 4, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 5379, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 5, 2, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 1, 4, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 3, 5, 2, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 3, 1, 4, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 5380, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 5, 3], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 5, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {1, 2, 3, 4}, {[0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 401, 1310, 4368, 14806, 50868, 176738, 619932, 2192288, 7807625, 27978530, 100809146, 364990184, 1327233335, 4845181810] "" "Class ", 5381, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1221, 3939, 12886, 42648, 142544, 480459, 1631287, 5574073, 19153815, 66146259, 229452587, 799140681, 2793373937] "" "Class ", 5382, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 2, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 5, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 5, 4, 2, 1], [0, 1, 0, 0]]} "Class ", 5383, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 2, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 5, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 2, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 5, 3], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 1, 0, 0]}], [[4, 3, 1, 2, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 376, 1168, 3678, 11716, 37688, 122261, 399533, 1314023, 4346226, 14447993, 48245641, 161758744, 544337525, 1837867537] "" "Class ", 5384, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 2, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 2, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {3, 4}, {[0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 366, 1105, 3356, 10251, 31483, 97186, 301431, 939004, 2936896, 9219531, 29040111, 91757034, 290754383, 923769926] "" "Class ", 5385, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1032, 2973, 8496, 24111, 68017, 190885, 533294, 1484021, 4115186, 11375765, 31358377, 86223943, 236540916] "" "Class ", 5386, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 2, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 5, 4, 2, 1], [0, 1, 1, 0]]} "Class ", 5387, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 2, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 2, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1032, 2973, 8496, 24111, 68017, 190885, 533294, 1484021, 4115186, 11375765, 31358377, 86223943, 236540916] "" "Class ", 5388, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 5, 3], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 5, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {2, 3, 4}, {[0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4158, 13873, 46893, 160247, 552723, 1921756, 6728347, 23701026, 83939765, 298712615, 1067598164, 3830414563] "" "Class ", 5389, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 5390, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 2, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 5, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 5, 4, 2, 1], [0, 1, 0, 1]]} "Class ", 5391, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 2, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 5, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 2, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 5, 3], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 5392, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 2, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 2, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 2, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {3, 4}, {[0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 366, 1105, 3356, 10251, 31483, 97186, 301431, 939004, 2936896, 9219531, 29040111, 91757034, 290754383, 923769926] "" "Class ", 5393, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 2, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 2, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1032, 2973, 8496, 24111, 68017, 190885, 533294, 1484021, 4115186, 11375765, 31358377, 86223943, 236540916] "" "Class ", 5394, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 2, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[3, 5, 4, 2, 1], [0, 1, 1, 1]]} "Class ", 5395, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 2, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 5, 4, 2, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1032, 2973, 8496, 24111, 68017, 190885, 533294, 1484021, 4115186, 11375765, 31358377, 86223943, 236540916] "" "Class ", 5396, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [ [4, 3, 1, 2, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4157, 13863, 46827, 159886, 550943, 1913526, 6691891, 23544320, 83280751, 295986327, 1056461081, 3785365874] "" "Class ", 5397, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 368, 1126, 3496, 11008, 35111, 113283, 369200, 1213879, 4021786, 13414608, 45009415, 151810413, 514428560, 1750508062] "" "Class ", 5398, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 2, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 4, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 3, 4, 2, 1], [0, 1, 0, 0]]} "Class ", 5399, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 2, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 4, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 3, 4, 2, 1], [1, 1, 0, 0]]} "Class ", 5400, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3, 5], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [ [4, 3, 1, 2, 5], {1, 3, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 3, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1032, 2973, 8496, 24111, 68017, 190885, 533294, 1484021, 4115186, 11375765, 31358377, 86223943, 236540916] "" "Class ", 5401, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 119, 334, 902, 2351, 5945, 14660, 35408, 84061, 196715, 454778, 1040522, 2359451, 5308589, 11862208, 26345684] "" "Class ", 5402, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 2, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 4, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 3, 4, 2, 1], [0, 1, 1, 0]]} "Class ", 5403, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 2, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 4, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 3, 4, 2, 1], [1, 1, 1, 0]]} "Class ", 5404, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}], [ [4, 3, 1, 2, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {2, 3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1220, 3929, 12822, 42309, 140922, 473169, 1599864, 5442561, 18615176, 63975857, 220816906, 765121477, 2660426630] "" "Class ", 5405, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {2, 3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 357, 1055, 3132, 9358, 28161, 85351, 260431, 799583, 2468725, 7660981, 23882778, 74762599, 234917916, 740685121] "" "Class ", 5406, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 2, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 4, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 3, 4, 2, 1], [0, 1, 0, 1]]} "Class ", 5407, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 2, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 4, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 3, 4, 2, 1], [1, 1, 0, 1]]} "Class ", 5408, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 2, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 4, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 2, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 4, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [ [4, 3, 1, 2, 5], {1, 3, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1032, 2973, 8496, 24111, 68017, 190885, 533294, 1484021, 4115186, 11375765, 31358377, 86223943, 236540916] "" "Class ", 5409, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 119, 334, 902, 2351, 5945, 14660, 35408, 84061, 196715, 454778, 1040522, 2359451, 5308589, 11862208, 26345684] "" "Class ", 5410, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 2, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 4, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 0]], [[5, 3, 4, 2, 1], [0, 1, 1, 1]]} "Class ", 5411, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 3, 2, 4, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 0]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]} "Class ", 5412, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 5, 4], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 5, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1265, 4148, 13808, 46542, 158534, 544869, 1887212, 6580775, 23083823, 81399079, 288380766, 1025982051, 3664054185] "" "Class ", 5413, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1221, 3939, 12886, 42648, 142544, 480459, 1631287, 5574073, 19153815, 66146259, 229452587, 799140681, 2793373937] "" "Class ", 5414, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 5, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 5, 4], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {1, 5}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1031, 2964, 8447, 23907, 67316, 188872, 528751, 1478571, 4133498, 11560364, 32361315, 90707911, 254649934] "" "Class ", 5415, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 2, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 5, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 2, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 5, 4], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1031, 2964, 8447, 23907, 67316, 188872, 528751, 1478571, 4133498, 11560364, 32361315, 90707911, 254649934] "" "Class ", 5416, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 5, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 5, 4], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 2, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 2, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 366, 1105, 3356, 10251, 31483, 97186, 301431, 939004, 2936896, 9219531, 29040111, 91757034, 290754383, 923769926] "" "Class ", 5417, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1032, 2973, 8496, 24111, 68017, 190885, 533294, 1484021, 4115186, 11375765, 31358377, 86223943, 236540916] "" "Class ", 5418, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 5, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 5, 4], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 119, 334, 902, 2351, 5945, 14660, 35408, 84061, 196715, 454778, 1040522, 2359451, 5308589, 11862208, 26345684] "" "Class ", 5419, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 2, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 5, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 2, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 5, 4], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 119, 334, 902, 2351, 5945, 14660, 35408, 84061, 196715, 454778, 1040522, 2359451, 5308589, 11862208, 26345684] "" "Class ", 5420, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {2, 3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1211, 3875, 12548, 41040, 135370, 449791, 1504057, 5057668, 17092030, 58018150, 197727023, 676290905, 2320721255] "" "Class ", 5421, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 5422, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {2, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {2, 5}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 120, 344, 960, 2608, 6912, 17920, 45568, 113920, 280576, 681984, 1638400, 3895296, 9175040, 21430272, 49676288] "" "Class ", 5423, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 2, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 2, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 120, 344, 960, 2608, 6912, 17920, 45568, 113920, 280576, 681984, 1638400, 3895296, 9175040, 21430272, 49676288] "" "Class ", 5424, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 2, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 2, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 2, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 366, 1105, 3356, 10251, 31483, 97186, 301431, 939004, 2936896, 9219531, 29040111, 91757034, 290754383, 923769926] "" "Class ", 5425, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 2, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 2, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1032, 2973, 8496, 24111, 68017, 190885, 533294, 1484021, 4115186, 11375765, 31358377, 86223943, 236540916] "" "Class ", 5426, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {2, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 119, 334, 902, 2351, 5945, 14660, 35408, 84061, 196715, 454778, 1040522, 2359451, 5308589, 11862208, 26345684] "" "Class ", 5427, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 2, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[4, 5, 3, 2, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 119, 334, 902, 2351, 5945, 14660, 35408, 84061, 196715, 454778, 1040522, 2359451, 5308589, 11862208, 26345684] "" "Class ", 5428, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {1, 2, 3, 4}, {[0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1265, 4147, 13798, 46476, 158170, 543050, 1878670, 6542330, 22915999, 80682987, 285378270, 1013564805, 3613262795] "" "Class ", 5429, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 361, 1094, 3368, 10519, 33269, 106362, 343193, 1116188, 3655336, 12043017, 39889065, 132747674, 443648571, 1488358040] "" "Class ", 5430, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {1, 5}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {4}, {[0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1031, 2964, 8447, 23907, 67316, 188872, 528751, 1478571, 4133498, 11560364, 32361315, 90707911, 254649934] "" "Class ", 5431, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {[1, 0, 0, 0, 0]}], [[4, 3, 2, 1, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 2, 3, 4}, { [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {4}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 118, 328, 886, 2353, 6207, 16379, 43415, 115825, 311204, 841999, 2292938, 6280965, 17296253, 47855169, 132967225] "" "Class ", 5432, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 2, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 2, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {3, 4}, {[0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 5433, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 118, 324, 845, 2106, 5059, 11807, 26948, 60455, 133820, 293110, 636615, 1373216, 2945265, 6286633, 13363382] "" "Class ", 5434, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {4}, {[0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 119, 334, 902, 2351, 5945, 14660, 35408, 84061, 196715, 454778, 1040522, 2359451, 5308589, 11862208, 26345684] "" "Class ", 5435, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {[1, 0, 0, 0, 0]}], [[4, 3, 2, 1, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 2, 3, 4}, { [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {4}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 116, 302, 715, 1549, 3106, 5831, 10352, 17525, 28484, 44696, 68021, 100777, 145810, 206569, 287186] "" "Class ", 5436, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {2, 3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {2, 3, 4}, {[0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1210, 3865, 12482, 40677, 133572, 441468, 1467296, 4900760, 16439370, 55357305, 187050302, 633998079, 2154950454] "" "Class ", 5437, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 120, 348, 1002, 2876, 8253, 23717, 68306, 197200, 570671, 1655112, 4810025, 14004288, 40840413, 119279153, 348837048] "" "Class ", 5438, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {2, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {2, 5}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {4}, {[0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 120, 344, 960, 2608, 6912, 17920, 45568, 113920, 280576, 681984, 1638400, 3895296, 9175040, 21430272, 49676288] "" "Class ", 5439, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {[1, 0, 0, 0, 0]}], [[4, 3, 2, 1, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {2, 3, 4}, { [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {2, 3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {4}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 117, 314, 789, 1872, 4242, 9279, 19768, 41307, 85123, 173704, 352063, 710266, 1428488, 2867125, 5747018] "" "Class ", 5440, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 2, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {3, 4}, {[0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 5441, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 118, 324, 845, 2106, 5059, 11807, 26948, 60455, 133820, 293110, 636615, 1373216, 2945265, 6286633, 13363382] "" "Class ", 5442, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {2, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {4}, {[0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 119, 334, 902, 2351, 5945, 14660, 35408, 84061, 196715, 454778, 1040522, 2359451, 5308589, 11862208, 26345684] "" "Class ", 5443, " is:" {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 0]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {[1, 0, 0, 0, 0]}], [[4, 3, 2, 1, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {2, 3, 4}, { [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {4}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 116, 302, 715, 1549, 3106, 5831, 10352, 17525, 28484, 44696, 68021, 100777, 145810, 206569, 287186] "" "Class ", 5444, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 2, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 5, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 827, 3795, 18755, 99146, 556711, 3305017, 20655285, 135399720, 927973061, 6631556521, 49294051497, 380306658250, 3039453750685, 25120541332271] "" "Class ", 5445, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 815, 3686, 17882, 92261, 503285, 2888967, 17374721, 109101403, 713172291, 4840150119, 34027903651, 247316785101, 1854946810551, 14334190857590] "" "Class ", 5446, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[1, 2, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 3, 5, 4], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 2, 4, 5, 3], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {3}, {[0, 0, 0, 0, 0, 1]}], [[1, 3, 5, 2, 4], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}] , [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 5, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [[2, 3, 5, 1, 4], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}] , [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 813, 3670, 17730, 91023, 493376, 2810318, 16748996, 104085499, 672420994, 4504180692, 31212168790, 223305392310, 1646525992254, 12492342876002] "" "Class ", 5447, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 0]]} "Class ", 5448, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]} "Class ", 5449, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3}, {[0, 0, 0, 0, 1]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {4}, {[0, 0, 0, 0, 0, 1]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 803, 3580, 17011, 85445, 450945, 2487846, 14287340, 85113784, 524416970, 3333334955, 21809961664, 146613104807, 1010887251462, 7138365114780] "" "Class ", 5450, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 1, 0]]} "Class ", 5451, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 0]]} "Class ", 5452, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 2, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 5, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 827, 3795, 18755, 99146, 556711, 3305017, 20655285, 135399720, 927973061, 6631556521, 49294051497, 380306658250, 3039453750685, 25120541332271] "" "Class ", 5453, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 815, 3686, 17882, 92261, 503285, 2888967, 17374721, 109101403, 713172291, 4840150119, 34027903651, 247316785101, 1854946810551, 14334190857590] "" "Class ", 5454, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {3}, {[0, 0, 0, 0, 1]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}] , [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}] , [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 813, 3670, 17730, 91023, 493376, 2810318, 16748996, 104085499, 672420994, 4504180692, 31212168790, 223305392310, 1646525992254, 12492342876002] "" "Class ", 5455, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]} "Class ", 5456, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 1, 1]]} "Class ", 5457, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3}, {[0, 0, 0, 0, 1]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {4}, {[0, 0, 0, 0, 0, 1]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 803, 3580, 17011, 85445, 450945, 2487846, 14287340, 85113784, 524416970, 3333334955, 21809961664, 146613104807, 1010887251462, 7138365114780] "" "Class ", 5458, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]} "Class ", 5459, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]} "Class ", 5460, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3, 4, 5], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3, 4, 5], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 863, 4001, 19917, 105594, 592404, 3498355, 21650945, 139914802, 941163116, 6572178283, 47531160988, 355285488652, 2739772751897, 21761249515981] "" "Class ", 5461, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 5, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3, 4, 5], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 3, 2, 1], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 3, 5, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 1, 3, 4, 5], [1, 1, 0, 0]]} "Class ", 5462, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3, 4, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3, 4, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {4}, {[0, 0, 0, 0, 1, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 862, 3982, 19687, 103253, 570458, 3301222, 19917370, 124799457, 809469329, 5419887379, 37372095432, 264834966743, 1925266539509, 14335251178399] "" "Class ", 5463, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 5, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3, 4, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 3, 2, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 3, 5, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 1, 3, 4, 5], [1, 1, 1, 0]]} "Class ", 5464, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3, 4, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3, 4, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 863, 4001, 19917, 105594, 592404, 3498355, 21650945, 139914802, 941163116, 6572178283, 47531160988, 355285488652, 2739772751897, 21761249515981] "" "Class ", 5465, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 5, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3, 4, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 3, 2, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 3, 5, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 1, 3, 4, 5], [1, 1, 0, 1]]} "Class ", 5466, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 5, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3, 4, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 3, 5, 4], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 5, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3, 4, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[1, 2, 3, 5, 4], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {4}, {[0, 0, 0, 0, 1, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 862, 3982, 19687, 103253, 570458, 3301222, 19917370, 124799457, 809469329, 5419887379, 37372095432, 264834966743, 1925266539509, 14335251178399] "" "Class ", 5467, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 5, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3, 4, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 3, 2, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 3, 5, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 1, 3, 4, 5], [1, 1, 1, 1]]} "Class ", 5468, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 4, 3, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 2, 4, 5], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 4, 2, 1], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 2, 3, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 4, 3, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 3, 2, 4, 5], [0, 1, 0, 0]]} "Class ", 5469, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 4, 3, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 2, 3, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 4, 3, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 0, 0]]} "Class ", 5470, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 4, 3, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 2, 4, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 4, 2, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 4, 3, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 3, 2, 4, 5], [0, 1, 1, 0]]} "Class ", 5471, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 4, 3, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 4, 3, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 1, 0]]} "Class ", 5472, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 4, 3, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 2, 4, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 4, 2, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 2, 3, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 4, 3, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 3, 2, 4, 5], [0, 1, 0, 1]]} "Class ", 5473, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 4, 3, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 2, 3, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 4, 3, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 0, 1]]} "Class ", 5474, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 4, 3, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 2, 4, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 4, 2, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 2, 3, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 4, 3, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 3, 2, 4, 5], [0, 1, 1, 1]]} "Class ", 5475, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 4, 3, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 2, 3, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 4, 3, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 1, 1]]} "Class ", 5476, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2, 4, 5], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2, 4, 5], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 863, 4001, 19917, 105594, 592404, 3498355, 21650945, 139914802, 941163116, 6572178283, 47531160988, 355285488652, 2739772751897, 21761249515981] "" "Class ", 5477, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 4, 5, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2, 4, 5], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 4, 2, 1], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 2, 1, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 4, 5, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 1, 2, 4, 5], [1, 1, 0, 0]]} "Class ", 5478, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2, 4, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2, 4, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2}, {[0, 0, 0, 1, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 862, 3982, 19687, 103253, 570458, 3301222, 19917370, 124799457, 809469329, 5419887379, 37372095432, 264834966743, 1925266539509, 14335251178399] "" "Class ", 5479, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 4, 5, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2, 4, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 4, 2, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 2, 1, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 4, 5, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 1, 2, 4, 5], [1, 1, 1, 0]]} "Class ", 5480, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2, 4, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2, 4, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 863, 4001, 19917, 105594, 592404, 3498355, 21650945, 139914802, 941163116, 6572178283, 47531160988, 355285488652, 2739772751897, 21761249515981] "" "Class ", 5481, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 4, 5, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2, 4, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 4, 2, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 2, 1, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 4, 5, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 1, 2, 4, 5], [1, 1, 0, 1]]} "Class ", 5482, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2, 4, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2, 4, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2}, {[0, 0, 0, 1, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 862, 3982, 19687, 103253, 570458, 3301222, 19917370, 124799457, 809469329, 5419887379, 37372095432, 264834966743, 1925266539509, 14335251178399] "" "Class ", 5483, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 4, 5, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2, 4, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 4, 2, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 2, 1, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 4, 5, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 1, 2, 4, 5], [1, 1, 1, 1]]} "Class ", 5484, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 5, 3, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1, 4, 5], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 5, 2, 1], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 1, 3, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 5, 3, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 3, 1, 4, 5], [0, 1, 0, 0]]} "Class ", 5485, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 5, 3, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1, 4, 5], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 5, 2, 1], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 1, 3, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 5, 3, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 3, 1, 4, 5], [1, 1, 0, 0]]} "Class ", 5486, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 5, 3, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1, 4, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 5, 2, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 1, 3, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 5, 3, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 3, 1, 4, 5], [0, 1, 1, 0]]} "Class ", 5487, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 5, 3, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1, 4, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 5, 2, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 5, 3, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 3, 1, 4, 5], [1, 1, 1, 0]]} "Class ", 5488, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 5, 3, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1, 4, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 5, 2, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 1, 3, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 5, 3, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 3, 1, 4, 5], [0, 1, 0, 1]]} "Class ", 5489, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 5, 3, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1, 4, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 5, 2, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 1, 3, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 5, 3, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 3, 1, 4, 5], [1, 1, 0, 1]]} "Class ", 5490, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 5, 3, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1, 4, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 5, 2, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 1, 3, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 5, 3, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 3, 1, 4, 5], [0, 1, 1, 1]]} "Class ", 5491, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 5, 3, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1, 4, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 5, 2, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 1, 3, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 5, 3, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 3, 1, 4, 5], [1, 1, 1, 1]]} "Class ", 5492, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 5, 4, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 1, 4, 5], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 5, 2, 1], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 1, 2, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 5, 4, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 2, 1, 4, 5], [1, 1, 0, 0]]} "Class ", 5493, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 5, 4, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 5, 2, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 5, 4, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 0]]} "Class ", 5494, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 5, 4, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 1, 4, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 5, 2, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 1, 2, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 5, 4, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 2, 1, 4, 5], [1, 1, 0, 1]]} "Class ", 5495, " is:" {{[[1, 3, 2], [1, 0]], [[1, 2, 5, 4, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 5, 2, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 2, 5, 4, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]} "Class ", 5496, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 2, 4, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3, 5], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 2, 3, 1], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 4, 2, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 2, 4, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3, 5], [0, 0, 1, 0]]} "Class ", 5497, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 2, 4, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 2, 3, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 4, 2, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 2, 4, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3, 5], [1, 0, 1, 0]]} "Class ", 5498, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 2, 4, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 4, 2, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 2, 4, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3, 5], [0, 1, 1, 0]]} "Class ", 5499, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 2, 4, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 4, 2, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 2, 4, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 1, 0]]} "Class ", 5500, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 2, 4, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 2, 3, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 4, 2, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 2, 4, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3, 5], [0, 0, 1, 1]]} "Class ", 5501, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 2, 4, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 2, 3, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 4, 2, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 2, 4, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3, 5], [1, 0, 1, 1]]} "Class ", 5502, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 2, 4, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 4, 2, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 2, 4, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3, 5], [0, 1, 1, 1]]} "Class ", 5503, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 2, 4, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 2, 4, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 1, 1]]} "Class ", 5504, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 2, 5, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 4, 3, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 2, 3, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 4, 1, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 2, 5, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[2, 1, 4, 3, 5], [1, 0, 1, 0]]} "Class ", 5505, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 2, 5, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 4, 1, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 2, 5, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 1, 0]]} "Class ", 5506, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 2, 5, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 4, 3, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 2, 3, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 4, 1, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 2, 5, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[2, 1, 4, 3, 5], [1, 0, 1, 1]]} "Class ", 5507, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 2, 5, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 4, 1, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 2, 5, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 1, 1]]} "Class ", 5508, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 4, 2, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 2, 3, 5], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 4, 3, 1], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 2, 4, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 4, 2, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 4, 2, 3, 5], [0, 1, 0, 0]]} "Class ", 5509, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 4, 2, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 4, 3, 1], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 2, 4, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 4, 2, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 0, 0]]} "Class ", 5510, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 4, 2, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 2, 3, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 4, 3, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 2, 4, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 4, 2, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 4, 2, 3, 5], [0, 1, 1, 0]]} "Class ", 5511, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 4, 2, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 4, 3, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 2, 4, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 4, 2, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 1, 0]]} "Class ", 5512, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 4, 2, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 2, 3, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 4, 3, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 2, 4, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 4, 2, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 4, 2, 3, 5], [0, 1, 0, 1]]} "Class ", 5513, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 4, 2, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 4, 3, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 2, 4, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 4, 2, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 0, 1]]} "Class ", 5514, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 4, 2, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 2, 3, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 4, 3, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 2, 4, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 4, 2, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 4, 2, 3, 5], [0, 1, 1, 1]]} "Class ", 5515, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 4, 2, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 4, 3, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 2, 4, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 4, 2, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 1, 1]]} "Class ", 5516, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 2, 3, 5], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 4, 3, 1], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 2, 3, 5], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 4, 3, 1], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {[0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 863, 4001, 19917, 105594, 592404, 3498355, 21650945, 139914802, 941163116, 6572178283, 47531160988, 355285488652, 2739772751897, 21761249515981] "" "Class ", 5517, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 4, 5, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 2, 3, 5], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 4, 3, 1], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 2, 1, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 4, 5, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 1, 2, 3, 5], [1, 1, 0, 0]]} "Class ", 5518, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 4, 5, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 2, 3, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 4, 3, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 2, 1, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 4, 5, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[4, 1, 2, 3, 5], [1, 0, 1, 0]]} "Class ", 5519, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 4, 5, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 2, 3, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 4, 3, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 2, 1, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 4, 5, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 1, 2, 3, 5], [1, 1, 1, 0]]} "Class ", 5520, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 2, 3, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 4, 3, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 2, 3, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 4, 3, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {[0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 863, 4001, 19917, 105594, 592404, 3498355, 21650945, 139914802, 941163116, 6572178283, 47531160988, 355285488652, 2739772751897, 21761249515981] "" "Class ", 5521, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 4, 5, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 2, 3, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 4, 3, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 2, 1, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 4, 5, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 1, 2, 3, 5], [1, 1, 0, 1]]} "Class ", 5522, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 4, 5, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 2, 3, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 4, 3, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 2, 1, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 4, 5, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[4, 1, 2, 3, 5], [1, 0, 1, 1]]} "Class ", 5523, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 4, 5, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 2, 3, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 4, 3, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 2, 1, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 4, 5, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 1, 2, 3, 5], [1, 1, 1, 1]]} "Class ", 5524, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 5, 2, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 1, 3, 5], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 5, 3, 1], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 1, 4, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 5, 2, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 4, 1, 3, 5], [0, 1, 0, 0]]} "Class ", 5525, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 5, 2, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 1, 3, 5], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 5, 3, 1], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 1, 4, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 5, 2, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 4, 1, 3, 5], [1, 1, 0, 0]]} "Class ", 5526, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 5, 2, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 1, 3, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 5, 3, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 1, 4, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 5, 2, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 4, 1, 3, 5], [0, 1, 1, 0]]} "Class ", 5527, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 5, 2, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 1, 3, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 5, 3, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 1, 4, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 5, 2, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 4, 1, 3, 5], [1, 1, 1, 0]]} "Class ", 5528, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 5, 2, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 1, 3, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 5, 3, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 1, 4, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 5, 2, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 4, 1, 3, 5], [0, 1, 0, 1]]} "Class ", 5529, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 5, 2, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 1, 3, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 5, 3, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 1, 4, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 5, 2, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 4, 1, 3, 5], [1, 1, 0, 1]]} "Class ", 5530, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 5, 2, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 1, 3, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 5, 3, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 1, 4, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 5, 2, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 4, 1, 3, 5], [0, 1, 1, 1]]} "Class ", 5531, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 5, 2, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 1, 3, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 5, 3, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 1, 4, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 5, 2, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 4, 1, 3, 5], [1, 1, 1, 1]]} "Class ", 5532, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 5, 4, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 1, 3, 5], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 5, 3, 1], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 1, 2, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 5, 4, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 2, 1, 3, 5], [1, 1, 0, 0]]} "Class ", 5533, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 5, 4, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 1, 3, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 5, 3, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 1, 2, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 5, 4, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 2, 1, 3, 5], [1, 1, 1, 0]]} "Class ", 5534, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 5, 4, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 1, 3, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 5, 3, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 1, 2, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 5, 4, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 2, 1, 3, 5], [1, 1, 0, 1]]} "Class ", 5535, " is:" {{[[1, 3, 2], [1, 0]], [[1, 3, 5, 4, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 1, 3, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 5, 3, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 3, 1, 2, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 3, 5, 4, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 2, 1, 3, 5], [1, 1, 1, 1]]} "Class ", 5536, " is:" {{[[1, 3, 2], [1, 0]], [[1, 4, 2, 3, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2, 5], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 2, 4, 1], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 2, 4, 3, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 4, 2, 3, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2, 5], [0, 0, 1, 0]]} "Class ", 5537, " is:" {{[[1, 3, 2], [1, 0]], [[1, 4, 2, 3, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 2, 4, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 2, 4, 3, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 4, 2, 3, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2, 5], [1, 0, 1, 0]]} "Class ", 5538, " is:" {{[[1, 3, 2], [1, 0]], [[1, 4, 2, 3, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 2, 4, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 2, 4, 3, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 4, 2, 3, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2, 5], [0, 1, 1, 0]]} "Class ", 5539, " is:" {{[[1, 3, 2], [1, 0]], [[1, 4, 2, 3, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 2, 4, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 2, 4, 3, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 4, 2, 3, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 1, 0]]} "Class ", 5540, " is:" {{[[1, 3, 2], [1, 0]], [[1, 4, 2, 3, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 2, 4, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 2, 4, 3, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 4, 2, 3, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2, 5], [0, 0, 1, 1]]} "Class ", 5541, " is:" {{[[1, 3, 2], [1, 0]], [[1, 4, 2, 3, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 2, 4, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 2, 4, 3, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 4, 2, 3, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2, 5], [1, 0, 1, 1]]} "Class ", 5542, " is:" {{[[1, 3, 2], [1, 0]], [[1, 4, 2, 3, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 2, 4, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 2, 4, 3, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 4, 2, 3, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2, 5], [0, 1, 1, 1]]} "Class ", 5543, " is:" {{[[1, 3, 2], [1, 0]], [[1, 4, 2, 3, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 2, 4, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 2, 4, 3, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 4, 2, 3, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 1, 1]]} "Class ", 5544, " is:" {{[[1, 3, 2], [1, 0]], [[1, 4, 2, 5, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 4, 2, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 2, 4, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 2, 4, 1, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 4, 2, 5, 3], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[3, 1, 4, 2, 5], [1, 0, 1, 0]]} "Class ", 5545, " is:" {{[[1, 3, 2], [1, 0]], [[1, 4, 2, 5, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 4, 2, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 2, 4, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 2, 4, 1, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 4, 2, 5, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 1, 4, 2, 5], [1, 1, 1, 0]]} "Class ", 5546, " is:" {{[[1, 3, 2], [1, 0]], [[1, 4, 2, 5, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 4, 2, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 2, 4, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 2, 4, 1, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 4, 2, 5, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[3, 1, 4, 2, 5], [1, 0, 1, 1]]} "Class ", 5547, " is:" {{[[1, 3, 2], [1, 0]], [[1, 4, 2, 5, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 4, 2, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 2, 4, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 2, 4, 1, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 4, 2, 5, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 1, 4, 2, 5], [1, 1, 1, 1]]} "Class ", 5548, " is:" {{[[1, 3, 2], [1, 0]], [[1, 4, 3, 2, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 3, 2, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 3, 4, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 2, 3, 4, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 4, 3, 2, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 4, 3, 2, 5], [0, 1, 1, 0]]} "Class ", 5549, " is:" {{[[1, 3, 2], [1, 0]], [[1, 4, 3, 2, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 3, 4, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 2, 3, 4, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 4, 3, 2, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 1, 0]]} "Class ", 5550, " is:" {{[[1, 3, 2], [1, 0]], [[1, 4, 3, 2, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 3, 2, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 3, 4, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 2, 3, 4, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 4, 3, 2, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 4, 3, 2, 5], [0, 1, 1, 1]]} "Class ", 5551, " is:" {{[[1, 3, 2], [1, 0]], [[1, 4, 3, 2, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 3, 4, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 2, 3, 4, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 4, 3, 2, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 1, 1]]} "Class ", 5552, " is:" {{[[1, 3, 2], [1, 0]], [[1, 4, 3, 5, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 3, 2, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 3, 4, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 2, 3, 1, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 4, 3, 5, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[4, 1, 3, 2, 5], [1, 0, 1, 0]]} "Class ", 5553, " is:" {{[[1, 3, 2], [1, 0]], [[1, 4, 3, 5, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 3, 2, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 3, 4, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 2, 3, 1, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 4, 3, 5, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 1, 3, 2, 5], [1, 1, 1, 0]]} "Class ", 5554, " is:" {{[[1, 3, 2], [1, 0]], [[1, 4, 3, 5, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 3, 2, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 3, 4, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 2, 3, 1, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 4, 3, 5, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[4, 1, 3, 2, 5], [1, 0, 1, 1]]} "Class ", 5555, " is:" {{[[1, 3, 2], [1, 0]], [[1, 4, 3, 5, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 3, 2, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 3, 4, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 2, 3, 1, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 4, 3, 5, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 1, 3, 2, 5], [1, 1, 1, 1]]} "Class ", 5556, " is:" {{[[1, 3, 2], [1, 0]], [[1, 4, 5, 2, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 1, 2, 5], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 5, 4, 1], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 2, 1, 4, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 4, 5, 2, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 4, 1, 2, 5], [0, 1, 0, 0]]} "Class ", 5557, " is:" {{[[1, 3, 2], [1, 0]], [[1, 4, 5, 2, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 1, 2, 5], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 5, 4, 1], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 2, 1, 4, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 4, 5, 2, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 4, 1, 2, 5], [1, 1, 0, 0]]} "Class ", 5558, " is:" {{[[1, 3, 2], [1, 0]], [[1, 4, 5, 2, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 1, 2, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 5, 4, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 2, 1, 4, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 4, 5, 2, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 4, 1, 2, 5], [0, 1, 1, 0]]} "Class ", 5559, " is:" {{[[1, 3, 2], [1, 0]], [[1, 4, 5, 2, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 1, 2, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 5, 4, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 2, 1, 4, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 4, 5, 2, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 4, 1, 2, 5], [1, 1, 1, 0]]} "Class ", 5560, " is:" {{[[1, 3, 2], [1, 0]], [[1, 4, 5, 2, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 1, 2, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 5, 4, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 2, 1, 4, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 4, 5, 2, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 4, 1, 2, 5], [0, 1, 0, 1]]} "Class ", 5561, " is:" {{[[1, 3, 2], [1, 0]], [[1, 4, 5, 2, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 1, 2, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 5, 4, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 2, 1, 4, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 4, 5, 2, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 4, 1, 2, 5], [1, 1, 0, 1]]} "Class ", 5562, " is:" {{[[1, 3, 2], [1, 0]], [[1, 4, 5, 2, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 1, 2, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 5, 4, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 2, 1, 4, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 4, 5, 2, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 4, 1, 2, 5], [0, 1, 1, 1]]} "Class ", 5563, " is:" {{[[1, 3, 2], [1, 0]], [[1, 4, 5, 2, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 1, 2, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 5, 4, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 2, 1, 4, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 4, 5, 2, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 4, 1, 2, 5], [1, 1, 1, 1]]} "Class ", 5564, " is:" {{[[1, 3, 2], [1, 0]], [[1, 4, 5, 3, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 3, 1, 2, 5], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 5, 4, 1], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 2, 1, 3, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 4, 5, 3, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 3, 1, 2, 5], [1, 1, 0, 0]]} "Class ", 5565, " is:" {{[[1, 3, 2], [1, 0]], [[1, 4, 5, 3, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 3, 1, 2, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 5, 4, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 2, 1, 3, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 4, 5, 3, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 3, 1, 2, 5], [1, 1, 1, 0]]} "Class ", 5566, " is:" {{[[1, 3, 2], [1, 0]], [[1, 4, 5, 3, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 3, 1, 2, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 5, 4, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 2, 1, 3, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 4, 5, 3, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 3, 1, 2, 5], [1, 1, 0, 1]]} "Class ", 5567, " is:" {{[[1, 3, 2], [1, 0]], [[1, 4, 5, 3, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 3, 1, 2, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 5, 4, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 2, 1, 3, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 4, 5, 3, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 3, 1, 2, 5], [1, 1, 1, 1]]} "Class ", 5568, " is:" {{[[1, 3, 2], [1, 0]], [[1, 5, 2, 3, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 4, 1, 5], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 2, 5, 1], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 1, 4, 3, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 5, 2, 3, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[2, 3, 4, 1, 5], [0, 0, 1, 0]]} "Class ", 5569, " is:" {{[[1, 3, 2], [1, 0]], [[1, 5, 2, 3, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 4, 1, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 2, 5, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 1, 4, 3, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 5, 2, 3, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[2, 3, 4, 1, 5], [1, 0, 1, 0]]} "Class ", 5570, " is:" {{[[1, 3, 2], [1, 0]], [[1, 5, 2, 3, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 4, 1, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 2, 5, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 1, 4, 3, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 5, 2, 3, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 3, 4, 1, 5], [0, 1, 1, 0]]} "Class ", 5571, " is:" {{[[1, 3, 2], [1, 0]], [[1, 5, 2, 3, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 4, 1, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 2, 5, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 1, 4, 3, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 5, 2, 3, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 3, 4, 1, 5], [1, 1, 1, 0]]} "Class ", 5572, " is:" {{[[1, 3, 2], [1, 0]], [[1, 5, 2, 3, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 4, 1, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 2, 5, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 1, 4, 3, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 5, 2, 3, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[2, 3, 4, 1, 5], [0, 0, 1, 1]]} "Class ", 5573, " is:" {{[[1, 3, 2], [1, 0]], [[1, 5, 2, 3, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 4, 1, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 2, 5, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 1, 4, 3, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 5, 2, 3, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[2, 3, 4, 1, 5], [1, 0, 1, 1]]} "Class ", 5574, " is:" {{[[1, 3, 2], [1, 0]], [[1, 5, 2, 3, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 4, 1, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 2, 5, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 1, 4, 3, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 5, 2, 3, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 3, 4, 1, 5], [0, 1, 1, 1]]} "Class ", 5575, " is:" {{[[1, 3, 2], [1, 0]], [[1, 5, 2, 3, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 4, 1, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 2, 5, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 1, 4, 3, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 5, 2, 3, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 3, 4, 1, 5], [1, 1, 1, 1]]} "Class ", 5576, " is:" {{[[1, 3, 2], [1, 0]], [[1, 5, 2, 4, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 4, 1, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 2, 5, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 1, 4, 2, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 5, 2, 4, 3], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[3, 2, 4, 1, 5], [1, 0, 1, 0]]} "Class ", 5577, " is:" {{[[1, 3, 2], [1, 0]], [[1, 5, 2, 4, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 4, 1, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 2, 5, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 1, 4, 2, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 5, 2, 4, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 2, 4, 1, 5], [1, 1, 1, 0]]} "Class ", 5578, " is:" {{[[1, 3, 2], [1, 0]], [[1, 5, 2, 4, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 4, 1, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 2, 5, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 1, 4, 2, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 5, 2, 4, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[3, 2, 4, 1, 5], [1, 0, 1, 1]]} "Class ", 5579, " is:" {{[[1, 3, 2], [1, 0]], [[1, 5, 2, 4, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 4, 1, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 2, 5, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 1, 4, 2, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 5, 2, 4, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 2, 4, 1, 5], [1, 1, 1, 1]]} "Class ", 5580, " is:" {{[[1, 3, 2], [1, 0]], [[1, 5, 3, 2, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 3, 1, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 3, 5, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 1, 3, 4, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 5, 3, 2, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 4, 3, 1, 5], [0, 1, 1, 0]]} "Class ", 5581, " is:" {{[[1, 3, 2], [1, 0]], [[1, 5, 3, 2, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 3, 1, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 3, 5, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 1, 3, 4, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 5, 3, 2, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 4, 3, 1, 5], [1, 1, 1, 0]]} "Class ", 5582, " is:" {{[[1, 3, 2], [1, 0]], [[1, 5, 3, 2, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 3, 1, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 3, 5, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 1, 3, 4, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 5, 3, 2, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 4, 3, 1, 5], [0, 1, 1, 1]]} "Class ", 5583, " is:" {{[[1, 3, 2], [1, 0]], [[1, 5, 3, 2, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 3, 1, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 3, 5, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 1, 3, 4, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 5, 3, 2, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 4, 3, 1, 5], [1, 1, 1, 1]]} "Class ", 5584, " is:" {{[[1, 3, 2], [1, 0]], [[1, 5, 3, 4, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 3, 1, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 3, 5, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 1, 3, 2, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 5, 3, 4, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[4, 2, 3, 1, 5], [1, 0, 1, 0]]} "Class ", 5585, " is:" {{[[1, 3, 2], [1, 0]], [[1, 5, 3, 4, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 3, 1, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 3, 5, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 1, 3, 2, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 5, 3, 4, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 2, 3, 1, 5], [1, 1, 1, 0]]} "Class ", 5586, " is:" {{[[1, 3, 2], [1, 0]], [[1, 5, 3, 4, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 3, 1, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 3, 5, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 1, 3, 2, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 5, 3, 4, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[4, 2, 3, 1, 5], [1, 0, 1, 1]]} "Class ", 5587, " is:" {{[[1, 3, 2], [1, 0]], [[1, 5, 3, 4, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 3, 1, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 3, 5, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 1, 3, 2, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 5, 3, 4, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 2, 3, 1, 5], [1, 1, 1, 1]]} "Class ", 5588, " is:" {{[[1, 3, 2], [1, 0]], [[1, 5, 4, 2, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 2, 1, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 4, 5, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 1, 2, 4, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 5, 4, 2, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 4, 2, 1, 5], [0, 1, 1, 0]]} "Class ", 5589, " is:" {{[[1, 3, 2], [1, 0]], [[1, 5, 4, 2, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 2, 1, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 4, 5, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 1, 2, 4, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 5, 4, 2, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 4, 2, 1, 5], [1, 1, 1, 0]]} "Class ", 5590, " is:" {{[[1, 3, 2], [1, 0]], [[1, 5, 4, 2, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 2, 1, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 4, 5, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 1, 2, 4, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[1, 5, 4, 2, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 4, 2, 1, 5], [0, 1, 1, 1]]} "Class ", 5591, " is:" {{[[1, 3, 2], [1, 0]], [[1, 5, 4, 2, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 2, 1, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 4, 5, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 1, 2, 4, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 5, 4, 2, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 4, 2, 1, 5], [1, 1, 1, 1]]} "Class ", 5592, " is:" {{[[1, 3, 2], [1, 0]], [[1, 5, 4, 3, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 3, 2, 1, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 4, 5, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[5, 1, 2, 3, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 5, 4, 3, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 3, 2, 1, 5], [1, 1, 1, 0]]} "Class ", 5593, " is:" {{[[1, 3, 2], [1, 0]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 4, 5, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]} "Class ", 5594, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}], [[2, 1, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 4, 5, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 831, 3842, 19196, 102916, 588348, 3568261, 22860864, 154147143, 1090390372, 8068679566, 62303006053, 500876641421, 4184041005138, 36250772580564] "" "Class ", 5595, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 3}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 819, 3738, 18386, 96787, 542178, 3217140, 20142200, 132611392, 915393336, 6607780456, 49763858162, 390188159825, 3179165732926, 26870933296010] "" "Class ", 5596, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[1, 2, 3, 4, 5], {3}, {}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {3}, {[0, 0, 0, 0, 0, 1]}], [[1, 3, 5, 2, 4], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}] , [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 5, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [[2, 3, 5, 1, 4], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}] , [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 818, 3725, 18255, 95591, 531728, 3127637, 19377980, 126044282, 858270061, 6102888205, 45217664110, 348415433122, 2787054423134, 23108239767575] "" "Class ", 5597, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 0, 0]]} "Class ", 5598, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 4, 5, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 819, 3733, 18310, 95915, 533331, 3132760, 19359287, 125413420, 849145785, 5993261559, 43992767730, 335157784756, 2645315254411, 21595189128148] "" "Class ", 5599, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 806, 3616, 17357, 88473, 476159, 2693373, 15951086, 98598252, 634434393, 4240033475, 29375404898, 210625353940, 1560711303298, 11936275985159] "" "Class ", 5600, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [0, 1, 1, 0]]} "Class ", 5601, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 1, 0]]} "Class ", 5602, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0]}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 789, 3495, 16545, 83142, 441009, 2457963, 14339835, 87281820, 552702609, 3632275683, 24719681601, 173880087210, 1261984254525, 9435921363783] "" "Class ", 5603, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0]}], [[1, 2, 4, 3], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 773, 3336, 15207, 72697, 362447, 1876392, 10051083, 55544661, 315899245, 1845139684, 11048651523, 67719859612, 424287619507, 2714074517843] "" "Class ", 5604, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}] , [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}] , [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 774, 3351, 15361, 74043, 373270, 1959528, 10673756, 60148231, 349756973, 2094116131, 12885558053, 81349014977, 526150688678, 3481840090140] "" "Class ", 5605, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 3, 2, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 0, 1]]} "Class ", 5606, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 3, 2, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 3, 2, 1], [1, 1, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0]}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 789, 3495, 16545, 83142, 441009, 2457963, 14339835, 87281820, 552702609, 3632275683, 24719681601, 173880087210, 1261984254525, 9435921363783] "" "Class ", 5607, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 3, 2, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 3, 2, 1], [1, 1, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0]}], [[1, 2, 4, 3], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 773, 3336, 15207, 72697, 362447, 1876392, 10051083, 55544661, 315899245, 1845139684, 11048651523, 67719859612, 424287619507, 2714074517843] "" "Class ", 5608, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 3, 2, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 3, 2, 1], [1, 1, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}] , [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}] , [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 774, 3351, 15361, 74043, 373270, 1959528, 10673756, 60148231, 349756973, 2094116131, 12885558053, 81349014977, 526150688678, 3481840090140] "" "Class ", 5609, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 3, 2, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 1, 1]]} "Class ", 5610, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 5, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3, 5, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 3, 1, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 3, 5, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 5, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3, 5, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 3, 1, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 1, 3, 5, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 864, 4020, 20155, 108094, 616533, 3721942, 23686249, 158360959, 1109015284, 8114024717, 61879321970, 490877181356, 4043104970827, 34517894735741] "" "Class ", 5611, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 5, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3, 5, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 3, 1, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 3, 5, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 1, 3, 5, 4], [1, 1, 0, 0]]} "Class ", 5612, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3, 5, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 3, 1, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3, 5, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 3, 1, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 862, 3985, 19747, 104031, 578926, 3385704, 20721629, 132266624, 877969218, 6045872826, 43101804636, 317557890913, 2414242111458, 18914531679092] "" "Class ", 5613, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 5, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3, 5, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 3, 1, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 3, 5, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 1, 3, 5, 4], [1, 1, 1, 0]]} "Class ", 5614, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 5, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3, 5, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 3, 1, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 3, 1, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 3, 5, 4], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 1]], [[2, 1, 3, 5, 4], [1, 0, 0, 1]]} "Class ", 5615, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 5, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3, 5, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 3, 1, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 3, 5, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 1, 3, 5, 4], [1, 1, 0, 1]]} "Class ", 5616, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 5, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3, 5, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 3, 1, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 3, 1, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 3, 5, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[2, 1, 3, 5, 4], [1, 0, 1, 1]]} "Class ", 5617, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 5, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3, 5, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 3, 1, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 3, 1, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 3, 5, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 1, 3, 5, 4], [1, 1, 1, 1]]} "Class ", 5618, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 4, 3, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 2, 5, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 4, 1, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 2, 3, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 4, 3, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 3, 2, 5, 4], [0, 1, 0, 0]]} "Class ", 5619, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 4, 3, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 2, 5, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 2, 3, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 4, 3, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 3, 2, 5, 4], [1, 1, 0, 0]]} "Class ", 5620, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 4, 3, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 2, 5, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 4, 1, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 4, 3, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 3, 2, 5, 4], [0, 1, 1, 0]]} "Class ", 5621, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 4, 3, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 2, 5, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 4, 3, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 3, 2, 5, 4], [1, 1, 1, 0]]} "Class ", 5622, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 4, 3, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 2, 5, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 4, 1, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 2, 3, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 4, 3, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 3, 2, 5, 4], [0, 1, 0, 1]]} "Class ", 5623, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 4, 3, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 2, 5, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 2, 3, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 4, 3, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 3, 2, 5, 4], [1, 1, 0, 1]]} "Class ", 5624, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 4, 3, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 2, 5, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 4, 1, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 2, 3, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 4, 3, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 3, 2, 5, 4], [0, 1, 1, 1]]} "Class ", 5625, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 4, 3, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 2, 5, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 2, 3, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 4, 3, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 3, 2, 5, 4], [1, 1, 1, 1]]} "Class ", 5626, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 4, 5, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2, 5, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 4, 1, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 4, 5, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 1, 4, 5, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2, 5, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 4, 1, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 1, 4, 5, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 3}, {[0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 864, 4020, 20155, 108094, 616533, 3721942, 23686249, 158360959, 1109015284, 8114024717, 61879321970, 490877181356, 4043104970827, 34517894735741] "" "Class ", 5627, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 4, 5, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2, 5, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 4, 1, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 2, 1, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 4, 5, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 1, 2, 5, 4], [1, 1, 0, 0]]} "Class ", 5628, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2, 5, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 4, 1, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2, 5, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 4, 1, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 862, 3985, 19747, 104031, 578926, 3385704, 20721629, 132266624, 877969218, 6045872826, 43101804636, 317557890913, 2414242111458, 18914531679092] "" "Class ", 5629, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 4, 5, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2, 5, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 4, 1, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 4, 5, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 1, 2, 5, 4], [1, 1, 1, 0]]} "Class ", 5630, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 4, 5, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2, 5, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 4, 1, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 2, 1, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 4, 5, 3], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 1]], [[3, 1, 2, 5, 4], [1, 0, 0, 1]]} "Class ", 5631, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 4, 5, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2, 5, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 4, 1, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 2, 1, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 4, 5, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 1, 2, 5, 4], [1, 1, 0, 1]]} "Class ", 5632, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 4, 5, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2, 5, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 4, 1, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 2, 1, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 4, 5, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[3, 1, 2, 5, 4], [1, 0, 1, 1]]} "Class ", 5633, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 4, 5, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2, 5, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 4, 1, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 2, 1, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 4, 5, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 1, 2, 5, 4], [1, 1, 1, 1]]} "Class ", 5634, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 5, 3, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1, 5, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 5, 1, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 1, 3, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 5, 3, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 3, 1, 5, 4], [0, 1, 0, 0]]} "Class ", 5635, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 5, 3, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1, 5, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 5, 1, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 1, 3, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 5, 3, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 3, 1, 5, 4], [1, 1, 0, 0]]} "Class ", 5636, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 5, 3, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1, 5, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 5, 1, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 1, 3, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 5, 3, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 3, 1, 5, 4], [0, 1, 1, 0]]} "Class ", 5637, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 5, 3, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1, 5, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 5, 1, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 1, 3, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 5, 3, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 3, 1, 5, 4], [1, 1, 1, 0]]} "Class ", 5638, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 5, 3, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1, 5, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 5, 1, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 1, 3, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 5, 3, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 3, 1, 5, 4], [0, 1, 0, 1]]} "Class ", 5639, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 5, 3, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1, 5, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 5, 1, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 1, 3, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 5, 3, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 3, 1, 5, 4], [1, 1, 0, 1]]} "Class ", 5640, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 5, 3, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1, 5, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 5, 1, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 1, 3, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 5, 3, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 3, 1, 5, 4], [0, 1, 1, 1]]} "Class ", 5641, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 5, 3, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1, 5, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 5, 1, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 1, 3, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 5, 3, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 3, 1, 5, 4], [1, 1, 1, 1]]} "Class ", 5642, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 5, 4, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 1, 5, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 5, 1, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 1, 2, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 5, 4, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 2, 1, 5, 4], [1, 1, 0, 0]]} "Class ", 5643, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 5, 4, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 1, 5, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 5, 1, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 5, 4, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 2, 1, 5, 4], [1, 1, 1, 0]]} "Class ", 5644, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 5, 4, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 1, 5, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 5, 1, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 1, 2, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 5, 4, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 2, 1, 5, 4], [1, 1, 0, 1]]} "Class ", 5645, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 5, 4, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 1, 5, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 5, 1, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 5, 1, 2, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 5, 4, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 2, 1, 5, 4], [1, 1, 1, 1]]} "Class ", 5646, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 3, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 3, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 3, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 3, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 831, 3843, 19205, 102993, 588979, 3573374, 22902192, 154486316, 1093230643, 8093018048, 62516809530, 502804344444, 4201888068327, 36420450427715] "" "Class ", 5647, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 3, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 3, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 820, 3747, 18461, 97385, 546813, 3253017, 20423456, 134856067, 933697656, 6760686409, 51074153740, 401714429827, 3283282946676, 27836746398232] "" "Class ", 5648, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 5, 2, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 5, 2, 1], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {4}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {4}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {4}, {}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {3, 4}, {}], [[3, 5, 1, 2, 4], {4}, {}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {}], [[4, 5, 1, 2, 3], {4}, {}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 799, 3577, 17160, 87607, 473331, 2694115, 16092976, 100559389, 655496474, 4446657704, 31325304206, 228740684791, 1728439184901, 13495130795651] "" "Class ", 5649, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 5, 2, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 5, 2, 1], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {4}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {4}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 5, 1, 2, 4], {4}, {}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {}], [[4, 5, 1, 2, 3], {4}, {}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 786, 3455, 16157, 79828, 414475, 2251807, 12756912, 75144750, 459145471, 2904137018, 18981839396, 128011946008, 889546078999, 6361655315141] "" "Class ", 5650, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 3, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 3, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 2, 5, 3, 4], [0, 0, 1, 0]]} "Class ", 5651, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 3, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 2, 5, 3, 4], [1, 0, 1, 0]]} "Class ", 5652, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 1, 0]]} "Class ", 5653, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 1, 0]]} "Class ", 5654, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 3, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 5, 2, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 3, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 5, 2, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 831, 3843, 19205, 102993, 588979, 3573374, 22902192, 154486316, 1093230643, 8093018048, 62516809530, 502804344444, 4201888068327, 36420450427715] "" "Class ", 5655, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 3, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 5, 2, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 3, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 5, 2, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 820, 3747, 18461, 97385, 546813, 3253017, 20423456, 134856067, 933697656, 6760686409, 51074153740, 401714429827, 3283282946676, 27836746398232] "" "Class ", 5656, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {4}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {4}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {4}, {}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {3, 4}, {}], [[3, 5, 1, 2, 4], {4}, {}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {}], [[4, 5, 1, 2, 3], {4}, {}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 799, 3577, 17160, 87607, 473331, 2694115, 16092976, 100559389, 655496474, 4446657704, 31325304206, 228740684791, 1728439184901, 13495130795651] "" "Class ", 5657, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {4}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {4}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 5, 1, 2, 4], {4}, {}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {}], [[4, 5, 1, 2, 3], {4}, {}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 786, 3455, 16157, 79828, 414475, 2251807, 12756912, 75144750, 459145471, 2904137018, 18981839396, 128011946008, 889546078999, 6361655315141] "" "Class ", 5658, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 3, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 3, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 5, 2, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 2, 5, 3, 4], [0, 0, 1, 1]]} "Class ", 5659, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 3, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 5, 2, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 2, 5, 3, 4], [1, 0, 1, 1]]} "Class ", 5660, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 5, 2, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 1, 1]]} "Class ", 5661, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 5, 2, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 1, 1]]} "Class ", 5662, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 5, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 5, 3, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 1, 3, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 1, 5, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 5, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 5, 3, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 1, 3, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 3, 1, 5, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 864, 4020, 20156, 108113, 616783, 3724785, 23716220, 158664528, 1112032112, 8143819462, 62174178045, 493817391486, 4072760820262, 34821261091580] "" "Class ", 5663, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 5, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 1, 5, 4], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 5, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 3, 1, 5, 4], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {4}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {4}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {4}, {[0, 0, 0, 0, 1, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 1, 2, 4], {4}, {}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {}], [[4, 5, 1, 2, 3], {4}, {}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 860, 3951, 19370, 100494, 548216, 3128836, 18607902, 114945311, 735547624, 4865140234, 33199767869, 233366837596, 1687376593869, 12535292304682] "" "Class ", 5664, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 5, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 5, 3, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 1, 3, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 5, 1, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 1, 5, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[2, 1, 5, 3, 4], [1, 0, 1, 0]]} "Class ", 5665, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 5, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 5, 1, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 1, 5, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 1, 0]]} "Class ", 5666, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 5, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 5, 3, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 1, 3, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 5, 1, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 1, 5, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 5, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 5, 3, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 1, 3, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 5, 1, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 3, 1, 5, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 864, 4020, 20156, 108113, 616783, 3724785, 23716220, 158664528, 1112032112, 8143819462, 62174178045, 493817391486, 4072760820262, 34821261091580] "" "Class ", 5667, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {4}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {4}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {4}, {[0, 0, 0, 0, 1, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 1, 2, 4], {4}, {}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {}], [[4, 5, 1, 2, 3], {4}, {}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 860, 3951, 19370, 100494, 548216, 3128836, 18607902, 114945311, 735547624, 4865140234, 33199767869, 233366837596, 1687376593869, 12535292304682] "" "Class ", 5668, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 5, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 5, 3, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 1, 3, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 5, 1, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 1, 5, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[2, 1, 5, 3, 4], [1, 0, 1, 1]]} "Class ", 5669, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 5, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 5, 1, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 1, 5, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 1, 1]]} "Class ", 5670, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 3, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 3, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 3, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 3, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {1, 2, 3}, {}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 831, 3843, 19205, 102993, 588979, 3573374, 22902192, 154486316, 1093230643, 8093018048, 62516809530, 502804344444, 4201888068327, 36420450427715] "" "Class ", 5671, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 786, 3458, 16203, 80311, 418797, 2287568, 13040865, 77352253, 476146324, 3034799869, 19988819454, 135818335121, 950548577932, 6842825911529] "" "Class ", 5672, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 3, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 3, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 5, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 5, 2, 3, 4], [0, 1, 0, 0]]} "Class ", 5673, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 5, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 0, 0]]} "Class ", 5674, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 3, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 3, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 5, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 3, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 3, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 5, 1], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {3}, {}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 822, 3773, 18697, 99336, 562446, 3377102, 21413687, 142875325, 999933787, 7320301453, 55919357148, 444749356803, 3675602224527, 31508214229320] "" "Class ", 5675, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 5, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 5, 1], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 773, 3338, 15241, 73084, 366139, 1908518, 10316665, 57677959, 332773524, 1977683814, 12088173127, 75890322627, 488810063426, 3226952233732] "" "Class ", 5676, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 3, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 3, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 5, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 5, 2, 3, 4], [0, 1, 1, 0]]} "Class ", 5677, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 5, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 1, 0]]} "Class ", 5678, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 3, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 3, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 5, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 3, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 3, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 5, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {1, 2, 3}, {}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 831, 3843, 19205, 102993, 588979, 3573374, 22902192, 154486316, 1093230643, 8093018048, 62516809530, 502804344444, 4201888068327, 36420450427715] "" "Class ", 5679, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 5, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 5, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 786, 3458, 16203, 80311, 418797, 2287568, 13040865, 77352253, 476146324, 3034799869, 19988819454, 135818335121, 950548577932, 6842825911529] "" "Class ", 5680, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 3, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 3, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 5, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 5, 2, 3, 4], [0, 1, 0, 1]]} "Class ", 5681, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 5, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 5, 1], [1, 0, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 4}, %1], [[2, 5, 1, 4, 3], {1, 2}, %1], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {4}, {[0, 0, 0, 0, 0, 1]}], [[3, 5, 1, 4, 2], {1, 2}, %1], [[3, 5, 2, 4, 1], {1, 2}, %1], [[4, 5, 1, 2, 3], {4}, {[0, 0, 0, 0, 0, 1]}], [[4, 5, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} %1 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 773, 3336, 15207, 72697, 362447, 1876392, 10051083, 55544661, 315899245, 1845139684, 11048651523, 67719859612, 424287619507, 2714074517843] "" "Class ", 5682, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 3, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 3, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 5, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 3, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 3, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 5, 1], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {3}, {}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 822, 3773, 18697, 99336, 562446, 3377102, 21413687, 142875325, 999933787, 7320301453, 55919357148, 444749356803, 3675602224527, 31508214229320] "" "Class ", 5683, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 5, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 5, 1], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 773, 3338, 15241, 73084, 366139, 1908518, 10316665, 57677959, 332773524, 1977683814, 12088173127, 75890322627, 488810063426, 3226952233732] "" "Class ", 5684, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 3, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 3, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 5, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 5, 2, 3, 4], [0, 1, 1, 1]]} "Class ", 5685, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 5, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 4, 1, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 1, 1]]} "Class ", 5686, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 2, 3, 4, 5], {2}, {}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 789, 3495, 16545, 83142, 441009, 2457963, 14339835, 87281820, 552702609, 3632275683, 24719681601, 173880087210, 1261984254525, 9435921363783] "" "Class ", 5687, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {}, {[1, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 2, 3, 4, 5], {1}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 789, 3495, 16545, 83142, 441009, 2457963, 14339835, 87281820, 552702609, 3632275683, 24719681601, 173880087210, 1261984254525, 9435921363783] "" "Class ", 5688, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 3, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 3, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {}, {[0, 0, 0, 0, 1]}], [[4, 1, 3, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 1, 3, 4, 2], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 773, 3336, 15207, 72697, 362447, 1876392, 10051083, 55544661, 315899245, 1845139684, 11048651523, 67719859612, 424287619507, 2714074517843] "" "Class ", 5689, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {}, {[0, 0, 0, 0, 1]}], [[4, 1, 3, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 1, 3, 4, 2], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 773, 3336, 15207, 72697, 362447, 1876392, 10051083, 55544661, 315899245, 1845139684, 11048651523, 67719859612, 424287619507, 2714074517843] "" "Class ", 5690, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 3, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [0, 0, 1, 0]]} "Class ", 5691, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 0]]} "Class ", 5692, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 3, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [0, 1, 1, 0]]} "Class ", 5693, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 0]]} "Class ", 5694, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 2, 3, 4, 5], {2}, {}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 789, 3495, 16545, 83142, 441009, 2457963, 14339835, 87281820, 552702609, 3632275683, 24719681601, 173880087210, 1261984254525, 9435921363783] "" "Class ", 5695, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 789, 3495, 16545, 83142, 441009, 2457963, 14339835, 87281820, 552702609, 3632275683, 24719681601, 173880087210, 1261984254525, 9435921363783] "" "Class ", 5696, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 3, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 3, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 773, 3336, 15207, 72697, 362447, 1876392, 10051083, 55544661, 315899245, 1845139684, 11048651523, 67719859612, 424287619507, 2714074517843] "" "Class ", 5697, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1, 5], [1, 0, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 773, 3336, 15207, 72697, 362447, 1876392, 10051083, 55544661, 315899245, 1845139684, 11048651523, 67719859612, 424287619507, 2714074517843] "" "Class ", 5698, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 3, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [0, 0, 1, 1]]} "Class ", 5699, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 1]]} "Class ", 5700, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 3, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [0, 1, 1, 1]]} "Class ", 5701, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 4, 5, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]} "Class ", 5702, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 3, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 3, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 1, 5, 2], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 3, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 3, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 1, 5, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {}], [[2, 3, 4, 1, 5], {1, 2, 3}, {}], [[2, 3, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 822, 3775, 18708, 99362, 562245, 3372683, 21356544, 142241471, 993342219, 7253513734, 55247151937, 437959067272, 3606339486556, 30792044130007] "" "Class ", 5703, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 3, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 3, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 1, 5, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 3, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 3, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 1, 5, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 786, 3458, 16203, 80311, 418797, 2287568, 13040865, 77352253, 476146324, 3034799869, 19988819454, 135818335121, 950548577932, 6842825911529] "" "Class ", 5704, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 3, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 3, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 1, 5, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 5, 1, 3, 4], [0, 1, 0, 0]]} "Class ", 5705, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 3, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 3, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 1, 5, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 5, 1, 3, 4], [1, 1, 0, 0]]} "Class ", 5706, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 3, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 3, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 1, 5, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 3, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 3, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 1, 5, 2], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 1, 5], {3}, {}], [[2, 3, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {3}, {}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 800, 3589, 17265, 88422, 479374, 2738190, 16413579, 102901389, 672740375, 4574837781, 32287364302, 236023161887, 1783897938017, 13918250870704] "" "Class ", 5707, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 3, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 3, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 1, 5, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 3, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 3, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 1, 5, 2], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 759, 3203, 14129, 64645, 304984, 1476932, 7315104, 36948515, 189871563, 990732313, 5240487838, 28060898517, 151925192982, 830830093074] "" "Class ", 5708, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 3, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 3, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 1, 5, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 5, 1, 3, 4], [0, 1, 1, 0]]} "Class ", 5709, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 3, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 3, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 1, 5, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 5, 1, 3, 4], [1, 1, 1, 0]]} "Class ", 5710, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 3, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 3, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 1, 5, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 3, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 3, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 1, 5, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {}], [[2, 3, 4, 1, 5], {1, 2, 3}, {}], [[2, 3, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 822, 3775, 18708, 99362, 562245, 3372683, 21356544, 142241471, 993342219, 7253513734, 55247151937, 437959067272, 3606339486556, 30792044130007] "" "Class ", 5711, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 3, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 3, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 1, 5, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 3, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 3, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 1, 5, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 786, 3458, 16203, 80311, 418797, 2287568, 13040865, 77352253, 476146324, 3034799869, 19988819454, 135818335121, 950548577932, 6842825911529] "" "Class ", 5712, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 3, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 3, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 1, 5, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 5, 1, 3, 4], [0, 1, 0, 1]]} "Class ", 5713, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 3, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 3, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 1, 5, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 5, 1, 3, 4], [1, 1, 0, 1]]} "Class ", 5714, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 3, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 3, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 1, 5, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 3, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 3, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 1, 5, 2], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 1, 5], {3}, {}], [[2, 3, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {3}, {}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 800, 3589, 17265, 88422, 479374, 2738190, 16413579, 102901389, 672740375, 4574837781, 32287364302, 236023161887, 1783897938017, 13918250870704] "" "Class ", 5715, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 3, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 3, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 1, 5, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 3, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 3, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 1, 5, 2], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 759, 3203, 14129, 64645, 304984, 1476932, 7315104, 36948515, 189871563, 990732313, 5240487838, 28060898517, 151925192982, 830830093074] "" "Class ", 5716, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 3, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 3, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 1, 5, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 5, 1, 3, 4], [0, 1, 1, 1]]} "Class ", 5717, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 3, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 3, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 1, 5, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 5, 1, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 5, 1, 3, 4], [1, 1, 1, 1]]} "Class ", 5718, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 5, 4, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 1, 3, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 5, 3, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 1, 2, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 5, 4, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 2, 1, 3, 4], [0, 1, 0, 0]]} "Class ", 5719, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 5, 4, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 1, 2, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 5, 4, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 0, 0]]} "Class ", 5720, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 5, 4, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 1, 3, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 5, 3, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 1, 2, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 5, 4, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 2, 1, 3, 4], [0, 1, 1, 0]]} "Class ", 5721, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 5, 4, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 1, 2, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 5, 4, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 1, 0]]} "Class ", 5722, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 5, 4, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 1, 3, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 5, 3, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 1, 2, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 5, 4, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 2, 1, 3, 4], [0, 1, 0, 1]]} "Class ", 5723, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 5, 4, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 1, 2, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 5, 4, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 0, 1]]} "Class ", 5724, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 5, 4, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 1, 3, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 5, 3, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 1, 2, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 5, 4, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 2, 1, 3, 4], [0, 1, 1, 1]]} "Class ", 5725, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 5, 4, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 3, 1, 2, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 5, 4, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 1, 1]]} "Class ", 5726, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 2, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 4, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 5, 3, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 2, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 4, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 5, 3, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 831, 3844, 19214, 103070, 589607, 3578454, 22943172, 154822048, 1096037721, 8117044062, 62727658830, 504703860310, 4219462588494, 36587450341658] "" "Class ", 5727, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 2, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 4, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 5, 3, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 2, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 4, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 5, 3, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 811, 3678, 17937, 93453, 517311, 3028339, 18675619, 120934018, 819960714, 5806564141, 42850878487, 328889995354, 2620674392796, 21644058974424] "" "Class ", 5728, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 2, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 4, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 5, 3, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 3, 5, 2, 4], [0, 1, 0, 0]]} "Class ", 5729, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 4, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 5, 3, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 0, 0]]} "Class ", 5730, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 2, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 4, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 5, 3, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 3, 5, 2, 4], [0, 0, 1, 0]]} "Class ", 5731, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 2, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 4, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 5, 3, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 3, 5, 2, 4], [1, 0, 1, 0]]} "Class ", 5732, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 2, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 4, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 5, 3, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 3, 5, 2, 4], [0, 1, 1, 0]]} "Class ", 5733, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 4, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 5, 3, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 1, 0]]} "Class ", 5734, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 2, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 4, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 5, 3, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 2, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 4, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 5, 3, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 4}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 822, 3776, 18718, 99445, 562893, 3377721, 21395837, 142552004, 995845879, 7274193198, 55422447455, 439485327846, 3619994280219, 30917584228699] "" "Class ", 5735, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 2, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 4, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 5, 3, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 2, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 4, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 5, 3, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 799, 3573, 17098, 86939, 467083, 2639162, 15622170, 96558495, 621425107, 4154067590, 28781416394, 206290295460, 1526992110546, 11655332503392] "" "Class ", 5736, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 2, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 4, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 5, 3, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 3, 5, 2, 4], [0, 1, 0, 1]]} "Class ", 5737, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 4, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 5, 3, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 0, 1]]} "Class ", 5738, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 2, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 4, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 5, 3, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 3, 5, 2, 4], [0, 0, 1, 1]]} "Class ", 5739, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 2, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 4, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 5, 3, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 3, 5, 2, 4], [1, 0, 1, 1]]} "Class ", 5740, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 2, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 4, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 5, 3, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 3, 5, 2, 4], [0, 1, 1, 1]]} "Class ", 5741, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 4, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 5, 3, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 1, 3, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 1, 1]]} "Class ", 5742, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 1, 5, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 5, 2, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 1, 4, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 1, 5, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 4, 1, 5, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 5, 2, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 1, 4, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 4, 1, 5, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 1, 0, 0]}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 864, 4021, 20171, 108268, 618192, 3736906, 23818173, 159518570, 1119234672, 8205376615, 62709548608, 498568249511, 4115850102439, 35221116485756] "" "Class ", 5743, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 1, 5, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 5, 2, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 1, 4, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 5, 1, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 1, 5, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 1, 5, 2, 4], [1, 1, 0, 0]]} "Class ", 5744, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 1, 5, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 5, 2, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 1, 4, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 5, 1, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 1, 5, 3], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[3, 1, 5, 2, 4], [1, 0, 1, 0]]} "Class ", 5745, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 1, 5, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 5, 2, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 1, 4, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 5, 1, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 1, 5, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 1, 5, 2, 4], [1, 1, 1, 0]]} "Class ", 5746, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 1, 5, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 5, 2, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 1, 4, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 5, 1, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 1, 5, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 4, 1, 5, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 5, 2, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 1, 4, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 5, 1, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 4, 1, 5, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 863, 4006, 20018, 106902, 606663, 3641807, 23037050, 153057907, 1065061437, 7742909230, 58679154724, 462648217251, 3788123136357, 32158164536753] "" "Class ", 5747, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 1, 5, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 5, 2, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 1, 4, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 5, 1, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 1, 5, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 1, 5, 2, 4], [1, 1, 0, 1]]} "Class ", 5748, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 1, 5, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 5, 2, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 1, 4, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 5, 1, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 1, 5, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[3, 1, 5, 2, 4], [1, 0, 1, 1]]} "Class ", 5749, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 1, 5, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 5, 2, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 1, 4, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 5, 1, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 1, 5, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 1, 5, 2, 4], [1, 1, 1, 1]]} "Class ", 5750, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 3, 1, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 3, 2, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 3, 4, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 3, 5, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 3, 1, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 5, 3, 2, 4], [0, 0, 1, 0]]} "Class ", 5751, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 3, 1, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 3, 2, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 3, 4, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 3, 5, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 3, 1, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 5, 3, 2, 4], [1, 0, 1, 0]]} "Class ", 5752, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 3, 1, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 3, 2, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 3, 4, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 3, 5, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 3, 1, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 5, 3, 2, 4], [0, 1, 1, 0]]} "Class ", 5753, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 3, 1, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 3, 5, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 3, 1, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 1, 0]]} "Class ", 5754, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 3, 1, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 3, 2, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 3, 4, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 3, 5, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 3, 1, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 5, 3, 2, 4], [0, 0, 1, 1]]} "Class ", 5755, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 3, 1, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 3, 2, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 3, 4, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 3, 5, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 3, 1, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 5, 3, 2, 4], [1, 0, 1, 1]]} "Class ", 5756, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 3, 1, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 3, 2, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 3, 4, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 3, 5, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 3, 1, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 5, 3, 2, 4], [0, 1, 1, 1]]} "Class ", 5757, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 3, 1, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 3, 5, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 3, 1, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 1, 1]]} "Class ", 5758, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 3, 5, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 3, 2, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 3, 4, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 3, 1, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 3, 5, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[5, 1, 3, 2, 4], [0, 0, 1, 0]]} "Class ", 5759, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 3, 5, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 3, 2, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 3, 1, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 3, 5, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[5, 1, 3, 2, 4], [1, 0, 1, 0]]} "Class ", 5760, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 3, 5, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 3, 2, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 3, 4, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 3, 1, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 3, 5, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 1, 3, 2, 4], [0, 1, 1, 0]]} "Class ", 5761, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 3, 5, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 3, 1, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 3, 5, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 1, 0]]} "Class ", 5762, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 3, 5, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 3, 2, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 3, 4, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 3, 1, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 3, 5, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[5, 1, 3, 2, 4], [0, 0, 1, 1]]} "Class ", 5763, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 3, 5, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 3, 2, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 3, 1, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 3, 5, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[5, 1, 3, 2, 4], [1, 0, 1, 1]]} "Class ", 5764, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 3, 5, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 3, 2, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 3, 4, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 3, 1, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 3, 5, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 1, 3, 2, 4], [0, 1, 1, 1]]} "Class ", 5765, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 3, 5, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 3, 1, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 3, 5, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 1, 1]]} "Class ", 5766, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 2, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 4, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 1, 5, 3], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 2, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 4, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 1, 5, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {}], [[1, 2, 3, 4, 5], {2}, {}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 1, 5], {1, 2, 3}, {}], [[2, 3, 4, 5, 1], {1}, {}], [[2, 3, 5, 1, 4], {1, 2, 3}, {}], [[2, 4, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 812, 3697, 18141, 95248, 532043, 3146604, 19623332, 128590735, 882726764, 6330813048, 47323820012, 367932786937, 2969612287858, 24838604316749] "" "Class ", 5767, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 2, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 4, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 1, 5, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 2, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 4, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 1, 5, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 1, 0, 0]}], [[1, 2, 3, 4, 5], {2}, {}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 5, 1], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 786, 3458, 16203, 80311, 418797, 2287568, 13040865, 77352253, 476146324, 3034799869, 19988819454, 135818335121, 950548577932, 6842825911529] "" "Class ", 5768, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 2, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 4, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 1, 5, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 5, 1, 2, 4], [0, 1, 0, 0]]} "Class ", 5769, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 2, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 4, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 1, 5, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 5, 1, 2, 4], [1, 1, 0, 0]]} "Class ", 5770, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 2, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 4, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 1, 5, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[3, 5, 1, 2, 4], [0, 0, 1, 0]]} "Class ", 5771, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 2, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 4, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 1, 5, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[3, 5, 1, 2, 4], [1, 0, 1, 0]]} "Class ", 5772, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 2, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 4, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 1, 5, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 5, 1, 2, 4], [0, 1, 1, 0]]} "Class ", 5773, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 2, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 4, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 1, 5, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 5, 1, 2, 4], [1, 1, 1, 0]]} "Class ", 5774, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 2, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 4, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 1, 5, 3], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 2, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 4, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 1, 5, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {}], [[2, 3, 4, 1, 5], {1, 2, 3}, {}], [[2, 3, 5, 1, 4], {1, 2, 3}, {}], [[2, 4, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 800, 3590, 17285, 88651, 481540, 2757054, 16572326, 104222912, 683756525, 4667432030, 33075450224, 242833458351, 1843754047659, 14453884061630] "" "Class ", 5775, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 2, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 4, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 1, 5, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 2, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 4, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 1, 5, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 773, 3336, 15207, 72697, 362447, 1876392, 10051083, 55544661, 315899245, 1845139684, 11048651523, 67719859612, 424287619507, 2714074517843] "" "Class ", 5776, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 2, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 4, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 1, 5, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 5, 1, 2, 4], [0, 1, 0, 1]]} "Class ", 5777, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 2, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 4, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 1, 5, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 5, 1, 2, 4], [1, 1, 0, 1]]} "Class ", 5778, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 2, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 4, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 1, 5, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[3, 5, 1, 2, 4], [0, 0, 1, 1]]} "Class ", 5779, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 2, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 4, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 1, 5, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[3, 5, 1, 2, 4], [1, 0, 1, 1]]} "Class ", 5780, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 2, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 4, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 1, 5, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 5, 1, 2, 4], [0, 1, 1, 1]]} "Class ", 5781, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 2, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 4, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 1, 5, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 5, 1, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 5, 1, 2, 4], [1, 1, 1, 1]]} "Class ", 5782, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 5, 3, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 1, 2, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 5, 4, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 1, 3, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 5, 3, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 3, 1, 2, 4], [0, 1, 0, 0]]} "Class ", 5783, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 5, 3, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 1, 2, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 1, 3, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 5, 3, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 3, 1, 2, 4], [1, 1, 0, 0]]} "Class ", 5784, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 5, 3, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 1, 2, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 5, 4, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 1, 3, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 5, 3, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 3, 1, 2, 4], [0, 1, 1, 0]]} "Class ", 5785, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 5, 3, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 1, 2, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 1, 3, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 5, 3, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 3, 1, 2, 4], [1, 1, 1, 0]]} "Class ", 5786, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 5, 3, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 1, 2, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 5, 4, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 1, 3, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 5, 3, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 3, 1, 2, 4], [0, 1, 0, 1]]} "Class ", 5787, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 5, 3, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 1, 2, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 1, 3, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 5, 3, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 3, 1, 2, 4], [1, 1, 0, 1]]} "Class ", 5788, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 5, 3, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 1, 2, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 5, 4, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 1, 3, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 5, 3, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 3, 1, 2, 4], [0, 1, 1, 1]]} "Class ", 5789, " is:" {{[[1, 3, 2], [1, 0]], [[2, 4, 5, 3, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 1, 2, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 2, 1, 3, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 4, 5, 3, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 3, 1, 2, 4], [1, 1, 1, 1]]} "Class ", 5790, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 1, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 5, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 5, 3, 2], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 1, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 5, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 5, 3, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[2, 4, 1, 3, 5], {1, 2}, {}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 822, 3773, 18687, 99174, 560661, 3359550, 21248136, 141338978, 985707612, 7187612397, 54665407330, 432700199078, 3557617692008, 30329249798962] "" "Class ", 5791, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 1, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 5, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 5, 3, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 1, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 5, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 5, 3, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 809, 3658, 17777, 92264, 508667, 2965700, 18217522, 117525431, 794037409, 5604546479, 41235381651, 315621530985, 2508699635377, 20672996632141] "" "Class ", 5792, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 1, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 5, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 5, 3, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 3, 5, 1, 4], [0, 1, 0, 0]]} "Class ", 5793, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 1, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 5, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 5, 3, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 3, 5, 1, 4], [1, 1, 0, 0]]} "Class ", 5794, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 1, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 5, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 5, 3, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[2, 3, 5, 1, 4], [0, 0, 1, 0]]} "Class ", 5795, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 1, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 5, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 5, 3, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[2, 3, 5, 1, 4], [1, 0, 1, 0]]} "Class ", 5796, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 1, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 5, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 5, 3, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 3, 5, 1, 4], [0, 1, 1, 0]]} "Class ", 5797, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 1, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 5, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 5, 3, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 3, 5, 1, 4], [1, 1, 1, 0]]} "Class ", 5798, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 1, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 5, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 5, 3, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 1, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 5, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 5, 3, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[2, 4, 1, 3, 5], {1, 2, 4}, {}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 800, 3590, 17285, 88647, 481475, 2756294, 16564596, 104149590, 683083964, 4661350288, 33020598433, 242336447952, 1839208890356, 14411807221290] "" "Class ", 5799, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 1, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 5, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 5, 3, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 1, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 5, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 5, 3, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 785, 3445, 16079, 79279, 410738, 2226579, 12585469, 73961451, 450801209, 2843790237, 18533224358, 124580268030, 862530562188, 6142898939668] "" "Class ", 5800, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 1, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 5, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 5, 3, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 3, 5, 1, 4], [0, 1, 0, 1]]} "Class ", 5801, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 1, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 5, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 5, 3, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 3, 5, 1, 4], [1, 1, 0, 1]]} "Class ", 5802, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 1, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 5, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 5, 3, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[2, 3, 5, 1, 4], [0, 0, 1, 1]]} "Class ", 5803, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 1, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 5, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 5, 3, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[2, 3, 5, 1, 4], [1, 0, 1, 1]]} "Class ", 5804, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 1, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 5, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 5, 3, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 3, 5, 1, 4], [0, 1, 1, 1]]} "Class ", 5805, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 1, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 5, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 5, 3, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 1, 3, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 3, 5, 1, 4], [1, 1, 1, 1]]} "Class ", 5806, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 1, 4, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 5, 1, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 1, 5, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 5, 2, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 1, 4, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 5, 1, 4, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 5, 1, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 1, 5, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 5, 2, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 5, 1, 4, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 863, 4006, 20017, 106866, 605988, 3632380, 22923735, 151799313, 1051655001, 7603073888, 57232590357, 447682041254, 3632381922991, 30521645665536] "" "Class ", 5807, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 1, 4, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 5, 1, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 1, 5, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 5, 2, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 1, 4, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 2, 5, 1, 4], [1, 1, 0, 0]]} "Class ", 5808, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 1, 4, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 5, 1, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 1, 5, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 5, 2, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 1, 4, 3], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[3, 2, 5, 1, 4], [1, 0, 1, 0]]} "Class ", 5809, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 1, 4, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 5, 1, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 1, 5, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 5, 2, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 1, 4, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 2, 5, 1, 4], [1, 1, 1, 0]]} "Class ", 5810, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 1, 4, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 5, 1, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 1, 5, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 5, 2, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 1, 4, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 5, 1, 4, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 5, 1, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 1, 5, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 5, 2, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 5, 1, 4, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 861, 3971, 19620, 103049, 571817, 3335642, 20372529, 129832059, 860877564, 5924446608, 42224529657, 311078259020, 2365010045511, 18526920132899] "" "Class ", 5811, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 1, 4, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 5, 1, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 1, 5, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 5, 2, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 1, 4, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 2, 5, 1, 4], [1, 1, 0, 1]]} "Class ", 5812, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 1, 4, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 5, 1, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 1, 5, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 5, 2, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 1, 4, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[3, 2, 5, 1, 4], [1, 0, 1, 1]]} "Class ", 5813, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 1, 4, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 5, 1, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 1, 5, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 5, 2, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 1, 4, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 2, 5, 1, 4], [1, 1, 1, 1]]} "Class ", 5814, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 3, 1, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 3, 1, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 3, 5, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 3, 5, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 3, 1, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[2, 5, 3, 1, 4], [0, 0, 1, 0]]} "Class ", 5815, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 3, 1, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 3, 1, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 3, 5, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 3, 5, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 3, 1, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[2, 5, 3, 1, 4], [1, 0, 1, 0]]} "Class ", 5816, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 3, 1, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 3, 1, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 3, 5, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 3, 5, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 3, 1, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 5, 3, 1, 4], [0, 1, 1, 0]]} "Class ", 5817, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 3, 1, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 3, 1, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 3, 5, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 3, 5, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 3, 1, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 5, 3, 1, 4], [1, 1, 1, 0]]} "Class ", 5818, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 3, 1, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 3, 1, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 3, 5, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 3, 5, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 3, 1, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[2, 5, 3, 1, 4], [0, 0, 1, 1]]} "Class ", 5819, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 3, 1, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 3, 1, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 3, 5, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 3, 5, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 3, 1, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[2, 5, 3, 1, 4], [1, 0, 1, 1]]} "Class ", 5820, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 3, 1, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 3, 1, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 3, 5, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 3, 5, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 3, 1, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 5, 3, 1, 4], [0, 1, 1, 1]]} "Class ", 5821, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 3, 1, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 3, 1, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 3, 5, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 3, 5, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 3, 1, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 5, 3, 1, 4], [1, 1, 1, 1]]} "Class ", 5822, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 3, 4, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 3, 1, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 3, 5, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 3, 2, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 3, 4, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[5, 2, 3, 1, 4], [0, 0, 1, 0]]} "Class ", 5823, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 3, 4, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 3, 1, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 3, 5, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 3, 2, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 3, 4, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[5, 2, 3, 1, 4], [1, 0, 1, 0]]} "Class ", 5824, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 3, 4, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 3, 1, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 3, 5, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 3, 2, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 3, 4, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 2, 3, 1, 4], [0, 1, 1, 0]]} "Class ", 5825, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 3, 4, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 3, 1, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 3, 2, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 3, 4, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 2, 3, 1, 4], [1, 1, 1, 0]]} "Class ", 5826, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 3, 4, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 3, 1, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 3, 5, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 3, 2, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 3, 4, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[5, 2, 3, 1, 4], [0, 0, 1, 1]]} "Class ", 5827, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 3, 4, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 3, 1, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 3, 5, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 3, 2, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 3, 4, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[5, 2, 3, 1, 4], [1, 0, 1, 1]]} "Class ", 5828, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 3, 4, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 3, 1, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 3, 5, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 3, 2, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 3, 4, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 2, 3, 1, 4], [0, 1, 1, 1]]} "Class ", 5829, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 3, 4, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 3, 1, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 3, 2, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 3, 4, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 2, 3, 1, 4], [1, 1, 1, 1]]} "Class ", 5830, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 4, 1, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 2, 1, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 4, 5, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 2, 5, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 4, 1, 3], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[3, 5, 2, 1, 4], [0, 0, 1, 0]]} "Class ", 5831, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 4, 1, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 2, 1, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 4, 5, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 2, 5, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 4, 1, 3], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[3, 5, 2, 1, 4], [1, 0, 1, 0]]} "Class ", 5832, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 4, 1, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 2, 1, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 4, 5, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 2, 5, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 4, 1, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 5, 2, 1, 4], [0, 1, 1, 0]]} "Class ", 5833, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 4, 1, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 2, 1, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 4, 5, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 2, 5, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 4, 1, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 5, 2, 1, 4], [1, 1, 1, 0]]} "Class ", 5834, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 4, 1, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 2, 1, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 4, 5, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 2, 5, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 4, 1, 3], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[3, 5, 2, 1, 4], [0, 0, 1, 1]]} "Class ", 5835, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 4, 1, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 2, 1, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 4, 5, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 2, 5, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 4, 1, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[3, 5, 2, 1, 4], [1, 0, 1, 1]]} "Class ", 5836, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 4, 1, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 2, 1, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 4, 5, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 2, 5, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 4, 1, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 5, 2, 1, 4], [0, 1, 1, 1]]} "Class ", 5837, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 4, 1, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 2, 1, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 4, 5, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 2, 5, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 4, 1, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 5, 2, 1, 4], [1, 1, 1, 1]]} "Class ", 5838, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 4, 3, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 2, 1, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 4, 5, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 2, 3, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 4, 3, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 3, 2, 1, 4], [0, 1, 1, 0]]} "Class ", 5839, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 4, 3, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 2, 3, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 4, 3, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 1, 0]]} "Class ", 5840, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 4, 3, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 2, 1, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 4, 5, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 2, 3, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 4, 3, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 3, 2, 1, 4], [0, 1, 1, 1]]} "Class ", 5841, " is:" {{[[1, 3, 2], [1, 0]], [[2, 5, 4, 3, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[4, 1, 2, 3, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 5, 4, 3, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 1, 1]]} "Class ", 5842, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 2, 1, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 4, 2, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 2, 1, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 4, 2, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {}, {}], [[4, 1, 2, 3], {1, 3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}], [[3, 1, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 3, 5, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 833, 3863, 19374, 104285, 598781, 3648198, 23481937, 159074336, 1130464776, 8403478065, 65178562910, 526276423689, 4414772583291, 38405762525639] "" "Class ", 5843, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 2, 1, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 4, 2, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 2, 1, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 4, 2, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {1, 3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 821, 3764, 18616, 98659, 556978, 3333035, 21053415, 139872382, 974337503, 7096675844, 53914336775, 426292960269, 3501177064554, 29816128527918] "" "Class ", 5844, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 4, 2, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 4, 2, 1], [0, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[1, 2, 3, 4, 5], {3}, {}], [[1, 2, 3, 5, 4], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {3}, {[0, 0, 0, 0, 0, 1]}], [[1, 3, 5, 2, 4], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}] , [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 5, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [[2, 3, 5, 1, 4], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}] , [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 811, 3681, 17972, 93723, 519061, 3038317, 18720920, 121001817, 817937217, 5767209374, 42317023078, 322450902430, 2546824237735, 20815539865689] "" "Class ", 5845, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 4, 2, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 0, 0]]} "Class ", 5846, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 2, 1, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 4, 2, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [0, 0, 1, 0]]} "Class ", 5847, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 2, 1, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 4, 2, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [1, 0, 1, 0]]} "Class ", 5848, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 4, 2, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 1, 0]]} "Class ", 5849, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 4, 2, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 1, 0]]} "Class ", 5850, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 4, 2, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 4, 2, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {1}, {[0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 789, 3495, 16545, 83142, 441009, 2457963, 14339835, 87281820, 552702609, 3632275683, 24719681601, 173880087210, 1261984254525, 9435921363783] "" "Class ", 5851, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 4, 2, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 4, 2, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {2}, {[0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 773, 3336, 15207, 72697, 362447, 1876392, 10051083, 55544661, 315899245, 1845139684, 11048651523, 67719859612, 424287619507, 2714074517843] "" "Class ", 5852, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 4, 2, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 4, 2, 1], [1, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {1}, {[0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}] , [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}] , [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 774, 3351, 15361, 74043, 373270, 1959528, 10673756, 60148231, 349756973, 2094116131, 12885558053, 81349014977, 526150688678, 3481840090140] "" "Class ", 5853, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 4, 2, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]} "Class ", 5854, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 2, 1, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 4, 2, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 2, 1, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 4, 2, 1], [1, 1, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {1}, {[0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 789, 3495, 16545, 83142, 441009, 2457963, 14339835, 87281820, 552702609, 3632275683, 24719681601, 173880087210, 1261984254525, 9435921363783] "" "Class ", 5855, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 2, 1, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 4, 2, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 2, 1, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 4, 2, 1], [1, 1, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {2}, {[0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 773, 3336, 15207, 72697, 362447, 1876392, 10051083, 55544661, 315899245, 1845139684, 11048651523, 67719859612, 424287619507, 2714074517843] "" "Class ", 5856, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 4, 2, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 4, 2, 1], [1, 1, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {1}, {[0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}] , [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}] , [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 774, 3351, 15361, 74043, 373270, 1959528, 10673756, 60148231, 349756973, 2094116131, 12885558053, 81349014977, 526150688678, 3481840090140] "" "Class ", 5857, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 4, 2, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 2, 4, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 1, 1]]} "Class ", 5858, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 5, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 4, 5, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 2, 1, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 4, 1, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 2, 5, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 5, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 4, 5, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 2, 1, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 4, 1, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 1, 2, 5, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 3}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {1, 3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 864, 4022, 20192, 108529, 620845, 3761693, 24041396, 161499985, 1136794308, 8362022447, 64123638649, 511530010683, 4236752990011, 36370369940823] "" "Class ", 5859, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 5, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 2, 1, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 4, 1, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 2, 5, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 0, 0]]} "Class ", 5860, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 5, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 4, 5, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 2, 1, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 4, 1, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 2, 5, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[2, 1, 4, 5, 3], [1, 0, 1, 0]]} "Class ", 5861, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 5, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 2, 1, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 4, 1, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 2, 5, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 1, 0]]} "Class ", 5862, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 5, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 4, 5, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 2, 1, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 4, 1, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 2, 5, 4], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 1]], [[2, 1, 4, 5, 3], [1, 0, 0, 1]]} "Class ", 5863, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 5, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 2, 1, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 4, 1, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 2, 5, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 0, 1]]} "Class ", 5864, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 5, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 4, 5, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 2, 1, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 4, 1, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 2, 5, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[2, 1, 4, 5, 3], [1, 0, 1, 1]]} "Class ", 5865, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 5, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 2, 1, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 4, 1, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 2, 5, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 1, 1]]} "Class ", 5866, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 4, 2, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 2, 5, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 4, 1, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 2, 4, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 4, 2, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 4, 2, 5, 3], [0, 1, 0, 0]]} "Class ", 5867, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 4, 2, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 2, 5, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 4, 1, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 2, 4, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 4, 2, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 4, 2, 5, 3], [1, 1, 0, 0]]} "Class ", 5868, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 4, 2, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 2, 5, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 4, 1, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 2, 4, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 4, 2, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 4, 2, 5, 3], [0, 1, 1, 0]]} "Class ", 5869, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 4, 2, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 2, 5, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 4, 1, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 2, 4, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 4, 2, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 4, 2, 5, 3], [1, 1, 1, 0]]} "Class ", 5870, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 4, 2, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 2, 5, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 4, 1, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 2, 4, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 4, 2, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 4, 2, 5, 3], [0, 1, 0, 1]]} "Class ", 5871, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 4, 2, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 2, 5, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 4, 1, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 2, 4, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 4, 2, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 4, 2, 5, 3], [1, 1, 0, 1]]} "Class ", 5872, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 4, 2, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 2, 5, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 4, 1, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 2, 4, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 4, 2, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 4, 2, 5, 3], [0, 1, 1, 1]]} "Class ", 5873, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 4, 2, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 2, 5, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 4, 1, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 2, 4, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 4, 2, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 4, 2, 5, 3], [1, 1, 1, 1]]} "Class ", 5874, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 4, 5, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 2, 5, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 4, 1, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 4, 5, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 1, 4, 5, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 2, 5, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 4, 1, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 1, 4, 5, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 3}, {[0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 864, 4022, 20191, 108507, 620557, 3758620, 24011631, 161226807, 1134369345, 8340959456, 63943572300, 510013699032, 4224232502995, 36270212955620] "" "Class ", 5875, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 4, 5, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 2, 5, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 4, 1, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 2, 1, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 4, 5, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 1, 2, 5, 3], [1, 1, 0, 0]]} "Class ", 5876, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 4, 5, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 2, 5, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 4, 1, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 2, 1, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 4, 5, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[4, 1, 2, 5, 3], [1, 0, 1, 0]]} "Class ", 5877, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 4, 5, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 2, 5, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 4, 1, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 2, 1, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 4, 5, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 1, 2, 5, 3], [1, 1, 1, 0]]} "Class ", 5878, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 4, 5, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 2, 5, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 4, 1, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 2, 1, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 4, 5, 2], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 1]], [[4, 1, 2, 5, 3], [1, 0, 0, 1]]} "Class ", 5879, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 4, 5, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 2, 5, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 4, 1, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 2, 1, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 4, 5, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 1, 2, 5, 3], [1, 1, 0, 1]]} "Class ", 5880, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 4, 5, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 2, 5, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 4, 1, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 2, 1, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 4, 5, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[4, 1, 2, 5, 3], [1, 0, 1, 1]]} "Class ", 5881, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 4, 5, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 2, 5, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 4, 1, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 2, 1, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 4, 5, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 1, 2, 5, 3], [1, 1, 1, 1]]} "Class ", 5882, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 5, 2, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 1, 5, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 5, 1, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 1, 4, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 5, 2, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 4, 1, 5, 3], [0, 1, 0, 0]]} "Class ", 5883, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 5, 2, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 1, 5, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 5, 1, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 1, 4, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 5, 2, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 4, 1, 5, 3], [1, 1, 0, 0]]} "Class ", 5884, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 5, 2, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 1, 5, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 5, 1, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 1, 4, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 5, 2, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 4, 1, 5, 3], [0, 1, 1, 0]]} "Class ", 5885, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 5, 2, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 1, 5, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 5, 1, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 1, 4, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 5, 2, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 4, 1, 5, 3], [1, 1, 1, 0]]} "Class ", 5886, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 5, 2, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 1, 5, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 5, 1, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 1, 4, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 5, 2, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 4, 1, 5, 3], [0, 1, 0, 1]]} "Class ", 5887, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 5, 2, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 1, 5, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 5, 1, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 1, 4, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 5, 2, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 4, 1, 5, 3], [1, 1, 0, 1]]} "Class ", 5888, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 5, 2, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 1, 5, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 5, 1, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 1, 4, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 5, 2, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 4, 1, 5, 3], [0, 1, 1, 1]]} "Class ", 5889, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 5, 2, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 1, 5, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 5, 1, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 1, 4, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 5, 2, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 4, 1, 5, 3], [1, 1, 1, 1]]} "Class ", 5890, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 5, 4, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 1, 5, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 5, 1, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 1, 2, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 5, 4, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 2, 1, 5, 3], [1, 1, 0, 0]]} "Class ", 5891, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 5, 4, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 1, 5, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 5, 1, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 1, 2, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 5, 4, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 2, 1, 5, 3], [1, 1, 1, 0]]} "Class ", 5892, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 5, 4, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 1, 5, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 5, 1, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 1, 2, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 5, 4, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 2, 1, 5, 3], [1, 1, 0, 1]]} "Class ", 5893, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 5, 4, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 1, 5, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 5, 1, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 5, 1, 2, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 5, 4, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 2, 1, 5, 3], [1, 1, 1, 1]]} "Class ", 5894, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 2, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 5, 2, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 2, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 5, 2, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 197, 842, 3933, 19893, 108121, 627370, 3865598, 25178941, 172706899, 1243305209, 9366291534, 73647024281, 603032072465, 5131305176936, 45290893655282] "" "Class ", 5895, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 2, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 5, 2, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 2, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 5, 2, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 831, 3846, 19261, 103626, 595245, 3631954, 23437119, 159343947, 1137593756, 8503224848, 66373188386, 539762316893, 4563567469816, 40038519320307] "" "Class ", 5896, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 5, 2, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 5, 2, 1], [0, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 2, 5, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 3, 5, 4, 2], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}] , [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 3, 5, 4, 1], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}] , [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 821, 3764, 18626, 98800, 558542, 3349263, 21216615, 141486335, 990217504, 7253424330, 55474842475, 442016753100, 3661924698057, 31486419683552] "" "Class ", 5897, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 5, 2, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 0, 0]]} "Class ", 5898, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 2, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [0, 0, 1, 0]]} "Class ", 5899, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 2, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 1, 0]]} "Class ", 5900, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 1, 0]]} "Class ", 5901, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 1, 0]]} "Class ", 5902, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 813, 3708, 18254, 96324, 541689, 3230758, 20351871, 134925540, 938453165, 6829022721, 51863722538, 410176883850, 3371468522443, 28749274772239] "" "Class ", 5903, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 799, 3581, 17243, 88662, 484494, 2802357, 17097889, 109705993, 738268791, 5198004310, 38206200009, 292566864237, 2329705957633, 19258209638253] "" "Class ", 5904, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}] , [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}] , [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 788, 3483, 16439, 82319, 435130, 2417958, 14077492, 85630390, 542902017, 3580263132, 24514983178, 174014618429, 1278688486281, 9714377846389] "" "Class ", 5905, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]} "Class ", 5906, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 2, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [0, 0, 1, 1]]} "Class ", 5907, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 2, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 1, 1]]} "Class ", 5908, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 1, 1]]} "Class ", 5909, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 1, 1]]} "Class ", 5910, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 1, 5, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 5, 4, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 1, 2, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 1, 5, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 1, 5, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 5, 4, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 1, 2, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 2, 1, 5, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 865, 4038, 20366, 110180, 635643, 3891392, 25173903, 171460598, 1225623414, 9168549007, 71598042013, 582342145729, 4923209846939, 43182872586602] "" "Class ", 5911, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 1, 5, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 5, 1, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 1, 5, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 0, 0]]} "Class ", 5912, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 1, 5, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 5, 4, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 1, 2, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 5, 1, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 1, 5, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[2, 1, 5, 4, 3], [1, 0, 1, 0]]} "Class ", 5913, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 1, 5, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 5, 1, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 1, 5, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 1, 0]]} "Class ", 5914, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 1, 5, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 5, 4, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 1, 2, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 5, 1, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 1, 5, 4], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 1]], [[2, 1, 5, 4, 3], [1, 0, 0, 1]]} "Class ", 5915, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 1, 5, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 1, 5, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 0, 1]]} "Class ", 5916, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 1, 5, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 5, 4, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 1, 2, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 5, 1, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 1, 5, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[2, 1, 5, 4, 3], [1, 0, 1, 1]]} "Class ", 5917, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 1, 5, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 5, 1, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 1, 5, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 1, 1]]} "Class ", 5918, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 2, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 2, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 3}, {}], [[4, 2, 5, 1, 3], {1, 2, 3}, {}], [[4, 3, 5, 1, 2], {1, 2, 3}, {}], [[4, 3, 5, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 197, 843, 3940, 19940, 108442, 629584, 3881149, 25291567, 173550929, 1249852171, 9418858983, 74083820900, 606785695218, 5164637615744, 45596479687870] "" "Class ", 5919, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 803, 3636, 17772, 93154, 520800, 3091330, 19403476, 128331240, 891527515, 6487291452, 49319621488, 390852154170, 3222137021132, 27580258122352] "" "Class ", 5920, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 2, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 1, 0, 0]]} "Class ", 5921, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 1, 3, 4, 5], {4}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 4, 5, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 777, 3401, 15911, 79190, 417802, 2329749, 13695329, 84675467, 549452299, 3734246560, 26529510525, 196651612573, 1518212302747, 12186977715559] "" "Class ", 5922, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 2, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 5, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 2, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 5, 1], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {2, 3}, {}], [[4, 2, 5, 1, 3], {2, 3}, {}], [[4, 3, 5, 1, 2], {2, 3}, {}], [[4, 3, 5, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 824, 3795, 18882, 100786, 573621, 3463425, 22089652, 148279285, 1044208046, 7692774559, 59140311960, 473391905603, 3937538560030, 33971104856852] "" "Class ", 5923, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 5, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 5, 1], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 775, 3369, 15560, 75865, 388518, 2081478, 11627872, 67548424, 407117735, 2540745606, 16390742041, 109139850833, 749101407315, 5293666521979] "" "Class ", 5924, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 2, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 5, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 1, 1, 0]]} "Class ", 5925, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 5, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 1, 0]]} "Class ", 5926, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 2, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 2, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 814, 3719, 18345, 97028, 546996, 3270726, 20657014, 137303930, 957453198, 6984945746, 53179741555, 421606207492, 3473612745569, 29688466628574] "" "Class ", 5927, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 763, 3270, 14844, 70961, 355673, 1862785, 10165879, 57673186, 339443431, 2068967527, 13039101751, 84846212977, 569306441734, 3934345877165] "" "Class ", 5928, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 2, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 1, 0, 1]]} "Class ", 5929, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {4}, {[0, 0, 0, 0, 0, 1]}], [[3, 5, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 5, 1, 2, 3], {4}, {[0, 0, 0, 0, 0, 1]}], [[4, 5, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 731, 2950, 12235, 51822, 223191, 974427, 4302645, 19181100, 86211885, 390248055, 1777495635, 8140539950, 37463689775, 173164232965] "" "Class ", 5930, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 2, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 5, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 2, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 5, 1], [1, 1, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 804, 3646, 17845, 93644, 523900, 3109648, 19501471, 128752376, 892078074, 6468403288, 48961942463, 386029724594, 3163823869930, 26905707777479] "" "Class ", 5931, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 5, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 5, 1], [1, 1, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 748, 3128, 13731, 62969, 300552, 1488704, 7634723, 40464741, 221311617, 1247444859, 7238458309, 43196661875, 264878725516, 1667564565616] "" "Class ", 5932, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 2, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [0, 1, 1, 1]]} "Class ", 5933, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {4}, {[0, 0, 0, 0, 0, 1]}], [[3, 5, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 5, 1, 2, 3], {4}, {[0, 0, 0, 0, 0, 1]}], [[4, 5, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 731, 2950, 12235, 51822, 223191, 974427, 4302645, 19181100, 86211885, 390248055, 1777495635, 8140539950, 37463689775, 173164232965] "" "Class ", 5934, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 2, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 2, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}], [[2, 1, 3, 4, 5], {1, 3, 4}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 4, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 805, 3664, 18048, 95542, 540291, 3246900, 20643189, 138316114, 973402948, 7173802441, 55220914682, 442934521578, 3694420386466, 31981769976026] "" "Class ", 5935, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 3}, {[1, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 792, 3548, 17132, 88631, 488782, 2860605, 17696907, 115322740, 789149714, 5654856366, 42326811420, 330189169352, 2679034414079, 22566187943683] "" "Class ", 5936, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 2, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 2, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1, 5], [0, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {}, {[0, 0, 0, 0, 1]}], [[4, 1, 3, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {3}, {[0, 0, 0, 0, 0, 1]}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 777, 3401, 15911, 79190, 417802, 2329749, 13695329, 84675467, 549452299, 3734246560, 26529510525, 196651612573, 1518212302747, 12186977715559] "" "Class ", 5937, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1, 5], [0, 0, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {}, {[0, 0, 0, 0, 1]}], [[4, 1, 3, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {3}, {[0, 0, 0, 0, 0, 1]}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 777, 3401, 15911, 79190, 417802, 2329749, 13695329, 84675467, 549452299, 3734246560, 26529510525, 196651612573, 1518212302747, 12186977715559] "" "Class ", 5938, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 2, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 2, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1, 5], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 3, 4, 5], {3}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 4, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 776, 3384, 15714, 77229, 399791, 2171587, 12338056, 73131336, 451218593, 2892521318, 19233706175, 132472590461, 943880653138, 6949363224560] "" "Class ", 5939, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 1, 0]]} "Class ", 5940, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 2, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [0, 1, 1, 0]]} "Class ", 5941, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 1, 0]]} "Class ", 5942, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 2, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 2, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 762, 3257, 14734, 70164, 350173, 1824916, 9900831, 55776020, 325541041, 1964740513, 12240641505, 78603636042, 519551554402, 3530432003317] "" "Class ", 5943, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 747, 3111, 13551, 61419, 288543, 1400727, 7008519, 36065919, 190531623, 1031674935, 5717624727, 32392623783, 187392817623, 1105868383095] "" "Class ", 5944, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 2, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 2, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 731, 2950, 12235, 51822, 223191, 974427, 4302645, 19181100, 86211885, 390248055, 1777495635, 8140539950, 37463689775, 173164232965] "" "Class ", 5945, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1, 5], [1, 0, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 731, 2950, 12235, 51822, 223191, 974427, 4302645, 19181100, 86211885, 390248055, 1777495635, 8140539950, 37463689775, 173164232965] "" "Class ", 5946, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 2, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 2, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1, 5], [1, 1, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 747, 3111, 13551, 61419, 288543, 1400727, 7008519, 36065919, 190531623, 1031674935, 5717624727, 32392623783, 187392817623, 1105868383095] "" "Class ", 5947, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1, 5], [1, 1, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 747, 3111, 13551, 61419, 288543, 1400727, 7008519, 36065919, 190531623, 1031674935, 5717624727, 32392623783, 187392817623, 1105868383095] "" "Class ", 5948, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 2, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 2, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1, 5], [1, 1, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 731, 2950, 12235, 51822, 223191, 974427, 4302645, 19181100, 86211885, 390248055, 1777495635, 8140539950, 37463689775, 173164232965] "" "Class ", 5949, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 5, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1, 5], [1, 1, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 731, 2950, 12235, 51822, 223191, 974427, 4302645, 19181100, 86211885, 390248055, 1777495635, 8140539950, 37463689775, 173164232965] "" "Class ", 5950, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 2, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 1, 5, 2], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 2, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 1, 5, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {}], [[3, 2, 4, 1, 5], {1, 2}, {}], [[3, 2, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {1, 2, 3}, {}], [[4, 3, 5, 1, 2], {1, 2, 3}, {}], [[4, 3, 5, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 834, 3877, 19511, 105498, 609049, 3734171, 24205801, 165255876, 1184280812, 8882580716, 69547988196, 567138264202, 4806784054194, 42264187628060] "" "Class ", 5951, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 4, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 2, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 1, 5, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 4, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 2, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 1, 5, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 802, 3624, 17669, 92371, 515095, 3050103, 19102976, 126101711, 874598117, 6355296794, 48260870870, 382106307860, 3147702631825, 26927530809779] "" "Class ", 5952, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 2, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 1, 5, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 1, 0, 0]]} "Class ", 5953, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 4, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 2, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 1, 5, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 4, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 2, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 1, 5, 2], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 1, 3, 4, 5], {4}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 4, 5, 1], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 789, 3504, 16694, 84844, 457903, 2614361, 15738974, 99622074, 661276128, 4592428258, 33297012678, 251545861356, 1976465482616, 16124678393524] "" "Class ", 5954, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 2, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 1, 5, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 2, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 1, 5, 2], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}], [[3, 2, 4, 1, 5], {2, 3}, {}], [[3, 2, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {2, 3}, {}], [[4, 3, 5, 1, 2], {2, 3}, {}], [[4, 3, 5, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 802, 3617, 17540, 90812, 499201, 2900235, 17738836, 113841627, 764379256, 5356205113, 39082761060, 296373524051, 2331608335586, 18999644737056] "" "Class ", 5955, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 4, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 2, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 1, 5, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 4, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 2, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 1, 5, 2], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 761, 3237, 14500, 67998, 332436, 1689268, 8902753, 48584899, 274240305, 1599727591, 9637474722, 59930980746, 384504930820, 2543948121073] "" "Class ", 5956, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 2, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 1, 5, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 1, 1, 0]]} "Class ", 5957, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 4, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 2, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 1, 5, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 5, 1, 4, 3], [1, 1, 1, 0]]} "Class ", 5958, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 2, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 1, 5, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 2, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 1, 5, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 803, 3630, 17672, 92038, 510001, 2992717, 18523342, 120516758, 821778232, 5857269211, 43536028506, 336745597373, 2705397629947, 22536656895194] "" "Class ", 5959, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 4, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 2, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 1, 5, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 1]], [[2, 5, 1, 4, 3], [1, 0, 0, 1]]} "Class ", 5960, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 2, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 1, 5, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 1, 0, 1]]} "Class ", 5961, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 4, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 2, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 1, 5, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 5, 1, 4, 3], [1, 1, 0, 1]]} "Class ", 5962, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 2, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 1, 5, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 0, 1, 1]]} "Class ", 5963, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 4, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 2, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 1, 5, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[2, 5, 1, 4, 3], [1, 0, 1, 1]]} "Class ", 5964, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 2, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 1, 5, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 5, 1, 4, 3], [0, 1, 1, 1]]} "Class ", 5965, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 1, 4, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 5, 2, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 1, 5, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 5, 1, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 5, 1, 4, 3], [1, 1, 1, 1]]} "Class ", 5966, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 5, 4, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 1, 4, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 5, 2, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 1, 2, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 5, 4, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 2, 1, 4, 3], [0, 1, 0, 0]]} "Class ", 5967, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 5, 4, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 1, 2, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 5, 4, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 0, 0]]} "Class ", 5968, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 5, 4, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 1, 4, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 5, 2, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 1, 2, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 5, 4, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 2, 1, 4, 3], [0, 1, 1, 0]]} "Class ", 5969, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 5, 4, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 1, 2, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 5, 4, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 1, 0]]} "Class ", 5970, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 5, 4, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 1, 4, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 5, 2, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 1, 2, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 5, 4, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 2, 1, 4, 3], [0, 1, 0, 1]]} "Class ", 5971, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 5, 4, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 1, 2, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 5, 4, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 0, 1]]} "Class ", 5972, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 5, 4, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 1, 4, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 5, 2, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 1, 2, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 5, 4, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 2, 1, 4, 3], [0, 1, 1, 1]]} "Class ", 5973, " is:" {{[[1, 3, 2], [1, 0]], [[3, 2, 5, 4, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 4, 1, 2, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 2, 5, 4, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 1, 1]]} "Class ", 5974, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 5, 4, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 5, 4, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2}, {}], [[4, 5, 1, 2, 3], {1, 2}, {}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 833, 3865, 19391, 104415, 599766, 3655696, 23539925, 159532177, 1134177265, 8434469955, 65445085406, 528637643563, 4436318001173, 38608164227151] "" "Class ", 5975, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 5, 4, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 5, 4, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 4, 1, 2, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 801, 3603, 17409, 89717, 490319, 2828263, 17149250, 108929751, 722622599, 4993308274, 35855713986, 267001933466, 2057991790812, 16391309150204] "" "Class ", 5976, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 1, 2, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 2, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 4, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 5, 4, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 1, 2, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 4, 5, 2, 3], [0, 1, 0, 0]]} "Class ", 5977, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 1, 2, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 5, 4, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 1, 2, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 0, 0]]} "Class ", 5978, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 1, 2, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 2, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 4, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 5, 4, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 1, 2, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 4, 5, 2, 3], [0, 0, 1, 0]]} "Class ", 5979, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 1, 2, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 5, 4, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 1, 2, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 1, 0]]} "Class ", 5980, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 1, 2, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 2, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 4, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 5, 4, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 1, 2, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 4, 5, 2, 3], [0, 1, 1, 0]]} "Class ", 5981, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 1, 2, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 5, 4, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 1, 2, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 1, 0]]} "Class ", 5982, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 1, 2, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 2, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 4, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 5, 4, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 1, 2, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 4, 5, 2, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 1, 2, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 2, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 4, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 5, 4, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 4, 5, 2, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 822, 3776, 18718, 99445, 562893, 3377721, 21395837, 142552004, 995845879, 7274193198, 55422447455, 439485327846, 3619994280219, 30917584228699] "" "Class ", 5983, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 1, 2, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 5, 4, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 1, 2, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 1, 2, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 5, 4, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 787, 3472, 16342, 81507, 428448, 2363239, 13628362, 81916773, 511861177, 3317336484, 22254329002, 154261222225, 1103135662707, 8126680213045] "" "Class ", 5984, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 1, 2, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 2, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 4, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 5, 4, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 1, 2, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 4, 5, 2, 3], [0, 1, 0, 1]]} "Class ", 5985, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 1, 2, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 5, 4, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 1, 2, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 0, 1]]} "Class ", 5986, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 1, 2, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 2, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 4, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 5, 4, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 1, 2, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 4, 5, 2, 3], [0, 0, 1, 1]]} "Class ", 5987, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 1, 2, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 4, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 5, 4, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 1, 2, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 4, 5, 2, 3], [1, 0, 1, 1]]} "Class ", 5988, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 1, 2, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 2, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 4, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 5, 4, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 1, 2, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 4, 5, 2, 3], [0, 1, 1, 1]]} "Class ", 5989, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 1, 2, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 4, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 5, 4, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 1, 2, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 4, 5, 2, 3], [1, 1, 1, 1]]} "Class ", 5990, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 1, 5, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 5, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 1, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 1, 5, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 1, 5, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 5, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 1, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 5, 1, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 4, 1, 5, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 864, 4022, 20192, 108525, 620779, 3761001, 24035534, 161459032, 1136595994, 8362289876, 64149290927, 512020992857, 4244113414553, 36470526181893] "" "Class ", 5991, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 1, 5, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 5, 2, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 1, 4, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 5, 1, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 1, 5, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 1, 5, 2, 3], [1, 1, 0, 0]]} "Class ", 5992, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 1, 5, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 5, 2, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 1, 4, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 5, 1, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 1, 5, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[4, 1, 5, 2, 3], [1, 0, 1, 0]]} "Class ", 5993, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 1, 5, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 5, 2, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 1, 4, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 5, 1, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 1, 5, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 1, 5, 2, 3], [1, 1, 1, 0]]} "Class ", 5994, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 1, 5, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 5, 2, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 1, 4, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 5, 1, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 1, 5, 2], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 1]], [[4, 1, 5, 2, 3], [1, 0, 0, 1]]} "Class ", 5995, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 1, 5, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 5, 2, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 1, 4, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 5, 1, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 1, 5, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 1, 5, 2, 3], [1, 1, 0, 1]]} "Class ", 5996, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 1, 5, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 5, 2, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 1, 4, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 5, 1, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 1, 5, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[4, 1, 5, 2, 3], [1, 0, 1, 1]]} "Class ", 5997, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 1, 5, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 5, 2, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 1, 4, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 5, 1, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 1, 5, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 1, 5, 2, 3], [1, 1, 1, 1]]} "Class ", 5998, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 5, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 5, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 197, 842, 3934, 19900, 108170, 627715, 3868057, 25196767, 172839943, 1244331171, 9374471772, 73714466855, 603606904949, 5136367513681, 45336923078533] "" "Class ", 5999, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 5, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 5, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 802, 3623, 17653, 92189, 513301, 3033553, 18954861, 124789946, 862961693, 6251100213, 47314277068, 373352221430, 3065106079087, 26131283750382] "" "Class ", 6000, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 2, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 4, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 5, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 5, 4, 2, 3], [0, 1, 0, 0]]} "Class ", 6001, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 5, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 5, 1], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {4}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {4}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {4}, {}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 5, 1, 2, 4], {4}, {}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[4, 5, 1, 2, 3], {4}, {}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 748, 3131, 13791, 63691, 307426, 1546303, 8083369, 43818190, 245844392, 1425343265, 8527833515, 52589056368, 333901296653, 2180589852782] "" "Class ", 6002, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 2, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 4, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 5, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 5, 4, 2, 3], [0, 0, 1, 0]]} "Class ", 6003, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 5, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 1, 0]]} "Class ", 6004, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 2, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 4, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 5, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 5, 4, 2, 3], [0, 1, 1, 0]]} "Class ", 6005, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 5, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 1, 0]]} "Class ", 6006, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 2, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 4, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 5, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 2, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 4, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 5, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 197, 842, 3934, 19900, 108170, 627715, 3868057, 25196767, 172839943, 1244331171, 9374471772, 73714466855, 603606904949, 5136367513681, 45336923078533] "" "Class ", 6007, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 5, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 5, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 802, 3623, 17653, 92189, 513301, 3033553, 18954861, 124789946, 862961693, 6251100213, 47314277068, 373352221430, 3065106079087, 26131283750382] "" "Class ", 6008, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 2, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 4, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 5, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 5, 4, 2, 3], [0, 1, 0, 1]]} "Class ", 6009, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 5, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 5, 1], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {4}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {4}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {4}, {}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 5, 1, 2, 4], {4}, {}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[4, 5, 1, 2, 3], {4}, {}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 748, 3131, 13791, 63691, 307426, 1546303, 8083369, 43818190, 245844392, 1425343265, 8527833515, 52589056368, 333901296653, 2180589852782] "" "Class ", 6010, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 2, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 4, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 5, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 5, 4, 2, 3], [0, 0, 1, 1]]} "Class ", 6011, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 4, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 5, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 5, 4, 2, 3], [1, 0, 1, 1]]} "Class ", 6012, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 2, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 4, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 5, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 5, 4, 2, 3], [0, 1, 1, 1]]} "Class ", 6013, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 4, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 5, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 2, 1, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 5, 4, 2, 3], [1, 1, 1, 1]]} "Class ", 6014, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[2, 3, 1, 4, 5], {1, 2, 4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 806, 3676, 18147, 96278, 545589, 3284991, 20921651, 140404227, 989530036, 7302336185, 56278854141, 451927473159, 3773340145222, 32696361672450] "" "Class ", 6015, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 793, 3562, 17262, 89684, 496894, 2922141, 18165176, 118937554, 817644030, 5885082985, 44237620651, 346498959821, 2822275646421, 23860709047645] "" "Class ", 6016, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 2, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 4, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 2, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 4, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {4}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {4}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {4}, {}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {4}, {}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {}], [[4, 5, 1, 2, 3], {4}, {}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 748, 3128, 13731, 62969, 300552, 1488704, 7634723, 40464741, 221311617, 1247444859, 7238458309, 43196661875, 264878725516, 1667564565616] "" "Class ", 6017, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 1, 5], [0, 0, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 0, 0, 1]}], [[4, 1, 3, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 3, 2], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [5, 2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 748, 3128, 13731, 62969, 300552, 1488704, 7634723, 40464741, 221311617, 1247444859, 7238458309, 43196661875, 264878725516, 1667564565616] "" "Class ", 6018, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 2, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 1, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[5, 1, 4, 2, 3], [0, 0, 1, 0]]} "Class ", 6019, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 1, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 1, 0]]} "Class ", 6020, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 2, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 4, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 1, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 1, 4, 2, 3], [0, 1, 1, 0]]} "Class ", 6021, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 1, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 1, 0]]} "Class ", 6022, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 2, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 1, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 2, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 1, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[2, 3, 1, 4, 5], {1, 2, 4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 806, 3676, 18147, 96278, 545589, 3284991, 20921651, 140404227, 989530036, 7302336185, 56278854141, 451927473159, 3773340145222, 32696361672450] "" "Class ", 6023, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 1, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 1, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 793, 3562, 17262, 89684, 496894, 2922141, 18165176, 118937554, 817644030, 5885082985, 44237620651, 346498959821, 2822275646421, 23860709047645] "" "Class ", 6024, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 2, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 4, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 1, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 2, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 4, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 1, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {4}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {4}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {4}, {}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {4}, {}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {}], [[4, 5, 1, 2, 3], {4}, {}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 748, 3128, 13731, 62969, 300552, 1488704, 7634723, 40464741, 221311617, 1247444859, 7238458309, 43196661875, 264878725516, 1667564565616] "" "Class ", 6025, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 1, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 1, 5], [1, 0, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 0, 0, 1]}], [[4, 1, 3, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 748, 3128, 13731, 62969, 300552, 1488704, 7634723, 40464741, 221311617, 1247444859, 7238458309, 43196661875, 264878725516, 1667564565616] "" "Class ", 6026, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 2, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 4, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 1, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[5, 1, 4, 2, 3], [0, 0, 1, 1]]} "Class ", 6027, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 4, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 1, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 0, 1, 1]]} "Class ", 6028, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 2, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 4, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 1, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 1, 4, 2, 3], [0, 1, 1, 1]]} "Class ", 6029, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 4, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 4, 1, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 2, 5, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 1, 4, 2, 3], [1, 1, 1, 1]]} "Class ", 6030, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 5, 4], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 5, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {}], [[1, 2, 3, 4, 5], {2}, {}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 1, 5], {1, 2, 3}, {}], [[2, 3, 4, 5, 1], {1}, {}], [[2, 3, 5, 1, 4], {1, 2, 3}, {}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[3, 4, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 803, 3633, 17713, 92392, 512432, 3006736, 18585150, 120577764, 818518898, 5797655988, 42744445432, 327316466860, 2598201270896, 21341945209278] "" "Class ", 6031, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 5, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 5, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[1, 2, 3, 4, 5], {2}, {}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 5, 1], {1, 2, 3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 788, 3482, 16418, 82022, 431693, 2382513, 13734791, 82433953, 513646512, 3314640426, 22105249150, 152063140806, 1077198511455, 7846233117110] "" "Class ", 6032, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 5, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 5, 4], [0, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 5, 2, 3, 1], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 774, 3354, 15409, 74579, 378365, 2004031, 11044492, 63155634, 373814565, 2285441155, 14406457695, 93478759539, 623459727530, 4268532434722] "" "Class ", 6033, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 5, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 5, 4], [0, 0, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 5, 2, 3, 1], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 774, 3354, 15409, 74579, 378365, 2004031, 11044492, 63155634, 373814565, 2285441155, 14406457695, 93478759539, 623459727530, 4268532434722] "" "Class ", 6034, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 4, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 5, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [0, 0, 1, 0]]} "Class ", 6035, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 4, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 5, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [1, 0, 1, 0]]} "Class ", 6036, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 5, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 1, 0]]} "Class ", 6037, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 5, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 1, 0]]} "Class ", 6038, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 4, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 5, 4], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 4, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 5, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 789, 3499, 16608, 83815, 447289, 2512790, 14803445, 91155779, 585044503, 3903910090, 27025083511, 193707381315, 1435096478925, 10972124319993] "" "Class ", 6039, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 4, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 5, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [1, 0, 0, 1]]} "Class ", 6040, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 5, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 5, 4], [1, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 759, 3210, 14245, 65919, 316605, 1572585, 8054555, 42439365, 229579255, 1272910376, 7223201657, 41896108289, 248107464451, 1498620699947] "" "Class ", 6041, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 5, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 5, 4], [1, 0, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 759, 3210, 14245, 65919, 316605, 1572585, 8054555, 42439365, 229579255, 1272910376, 7223201657, 41896108289, 248107464451, 1498620699947] "" "Class ", 6042, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 4, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 5, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [0, 0, 1, 1]]} "Class ", 6043, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 4, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 5, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [1, 0, 1, 1]]} "Class ", 6044, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 4, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 5, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]} "Class ", 6045, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 4, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 5, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 5, 1, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 5, 1, 2, 3], [1, 1, 1, 1]]} "Class ", 6046, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {}], [[2, 3, 4, 1, 5], {1, 2, 3}, {}], [[2, 3, 5, 1, 4], {1, 2, 3}, {}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 805, 3663, 18033, 95391, 538961, 3235819, 20552641, 137575157, 967260203, 7121871831, 54771540205, 438945818425, 3658065146939, 31641349312421] "" "Class ", 6047, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 747, 3111, 13551, 61419, 288543, 1400727, 7008519, 36065919, 190531623, 1031674935, 5717624727, 32392623783, 187392817623, 1105868383095] "" "Class ", 6048, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 0, 0]]} "Class ", 6049, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4, 5], [0, 0, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {2}, {[0, 0, 0, 1]}], [[3, 2, 1], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [5, 4, 2, 3, 1], {1, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 747, 3111, 13551, 61419, 288543, 1400727, 7008519, 36065919, 190531623, 1031674935, 5717624727, 32392623783, 187392817623, 1105868383095] "" "Class ", 6050, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 4, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 4, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4, 5], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 1, 5], {3}, {}], [[2, 3, 5, 1, 4], {3}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {3}, {}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 792, 3552, 17209, 89557, 498009, 2945120, 18443269, 121837899, 846175809, 6159706818, 46871718649, 371934644984, 3071052254110, 26334454360267] "" "Class ", 6051, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4, 5], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2, 3, 4}, {[1, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 731, 2950, 12235, 51822, 223191, 974427, 4302645, 19181100, 86211885, 390248055, 1777495635, 8140539950, 37463689775, 173164232965] "" "Class ", 6052, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 1, 0]]} "Class ", 6053, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4, 5], [0, 1, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {2}, {[0, 0, 0, 1]}], [[3, 2, 1], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [5, 4, 2, 3, 1], {1, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 731, 2950, 12235, 51822, 223191, 974427, 4302645, 19181100, 86211885, 390248055, 1777495635, 8140539950, 37463689775, 173164232965] "" "Class ", 6054, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 4, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 4, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {}], [[2, 3, 4, 1, 5], {1, 2, 3}, {}], [[2, 3, 5, 1, 4], {1, 2, 3}, {}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 805, 3663, 18033, 95391, 538961, 3235819, 20552641, 137575157, 967260203, 7121871831, 54771540205, 438945818425, 3658065146939, 31641349312421] "" "Class ", 6055, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 747, 3111, 13551, 61419, 288543, 1400727, 7008519, 36065919, 190531623, 1031674935, 5717624727, 32392623783, 187392817623, 1105868383095] "" "Class ", 6056, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 0, 0, 1]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [5, 3, 4, 1, 2], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [ [5, 3, 4, 2, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 788, 3487, 16502, 83009, 441669, 2475744, 14570574, 89771917, 577545145, 3871035502, 26976190952, 195095969405, 1461856430788, 11331491694638] "" "Class ", 6057, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {2}, {[0, 0, 0, 1]}], [[3, 2, 1], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 747, 3111, 13551, 61419, 288543, 1400727, 7008519, 36065919, 190531623, 1031674935, 5717624727, 32392623783, 187392817623, 1105868383095] "" "Class ", 6058, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 4, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 4, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4, 5], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 1, 5], {3}, {}], [[2, 3, 5, 1, 4], {3}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {3}, {}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 792, 3552, 17209, 89557, 498009, 2945120, 18443269, 121837899, 846175809, 6159706818, 46871718649, 371934644984, 3071052254110, 26334454360267] "" "Class ", 6059, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 4, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4, 5], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2, 3, 4}, {[1, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 731, 2950, 12235, 51822, 223191, 974427, 4302645, 19181100, 86211885, 390248055, 1777495635, 8140539950, 37463689775, 173164232965] "" "Class ", 6060, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 4, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]} "Class ", 6061, " is:" {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 5, 2, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 4, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {2}, {[0, 0, 0, 1]}], [[3, 2, 1], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 731, 2950, 12235, 51822, 223191, 974427, 4302645, 19181100, 86211885, 390248055, 1777495635, 8140539950, 37463689775, 173164232965] "" "Class ", 6062, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 1, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 5, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 5, 4, 2], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 1, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 5, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 5, 4, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[3, 4, 1, 2, 5], {1, 2}, {}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2}, {}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 824, 3800, 18942, 101275, 577305, 3490768, 22292682, 149797104, 1055678533, 7780593188, 59821283240, 478728214545, 3979614222165, 34302464950263] "" "Class ", 6063, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 1, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 5, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 5, 4, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 1, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 5, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 5, 4, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 5, 1, 2, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 800, 3592, 17320, 89066, 485718, 2795892, 16919320, 107268640, 710366353, 4900736260, 35139052663, 261311833567, 2011650170181, 16004211114050] "" "Class ", 6064, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 1, 2, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 1, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 5, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 5, 4, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 1, 2, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 4, 5, 1, 3], [0, 1, 0, 0]]} "Class ", 6065, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 1, 2, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 1, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 5, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 5, 4, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 1, 2, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 4, 5, 1, 3], [1, 1, 0, 0]]} "Class ", 6066, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 1, 2, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 1, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 5, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 5, 4, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 1, 2, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[2, 4, 5, 1, 3], [0, 0, 1, 0]]} "Class ", 6067, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 1, 2, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 1, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 5, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 5, 4, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 1, 2, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[2, 4, 5, 1, 3], [1, 0, 1, 0]]} "Class ", 6068, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 1, 2, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 1, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 5, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 5, 4, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 1, 2, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 4, 5, 1, 3], [0, 1, 1, 0]]} "Class ", 6069, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 1, 2, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 1, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 5, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 5, 4, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 1, 2, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 4, 5, 1, 3], [1, 1, 1, 0]]} "Class ", 6070, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 1, 2, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 1, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 5, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 5, 4, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 1, 2, 4], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 1]], [[2, 4, 5, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 5, 1, 2, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 1, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 5, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 5, 4, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[2, 4, 5, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 800, 3590, 17285, 88647, 481475, 2756294, 16564596, 104149590, 683083964, 4661350288, 33020598433, 242336447952, 1839208890356, 14411807221290] "" "Class ", 6071, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 1, 2, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 1, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 5, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 5, 4, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 1, 2, 4], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 1]], [[2, 4, 5, 1, 3], [1, 0, 0, 1]]} "Class ", 6072, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 1, 2, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 1, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 5, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 5, 4, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 1, 2, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 4, 5, 1, 3], [0, 1, 0, 1]]} "Class ", 6073, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 1, 2, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 1, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 5, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 5, 4, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 1, 2, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 4, 5, 1, 3], [1, 1, 0, 1]]} "Class ", 6074, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 1, 2, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 1, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 5, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 5, 4, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 1, 2, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[2, 4, 5, 1, 3], [0, 0, 1, 1]]} "Class ", 6075, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 1, 2, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 1, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 5, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 5, 4, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 1, 2, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[2, 4, 5, 1, 3], [1, 0, 1, 1]]} "Class ", 6076, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 1, 2, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 1, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 5, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 5, 4, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 1, 2, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 4, 5, 1, 3], [0, 1, 1, 1]]} "Class ", 6077, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 1, 2, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 1, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 5, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 5, 4, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 1, 2, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 4, 5, 1, 3], [1, 1, 1, 1]]} "Class ", 6078, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 1, 4, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 5, 1, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 1, 5, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 5, 2, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 1, 4, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 5, 1, 4, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 5, 1, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 1, 5, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 5, 2, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 5, 1, 4, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 863, 4007, 20040, 107171, 609223, 3663480, 23210286, 154397817, 1075174748, 7817367510, 59208790620, 466193897681, 3808933312886, 32238531263335] "" "Class ", 6079, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 1, 4, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 5, 1, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 1, 5, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 5, 2, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 1, 4, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 2, 5, 1, 3], [1, 1, 0, 0]]} "Class ", 6080, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 1, 4, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 5, 1, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 1, 5, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 5, 2, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 1, 4, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[4, 2, 5, 1, 3], [1, 0, 1, 0]]} "Class ", 6081, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 1, 4, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 5, 1, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 1, 5, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 5, 2, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 1, 4, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 2, 5, 1, 3], [1, 1, 1, 0]]} "Class ", 6082, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 1, 4, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 5, 1, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 1, 5, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 5, 2, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 1, 4, 2], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 1]], [[4, 2, 5, 1, 3], [1, 0, 0, 1]]} "Class ", 6083, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 1, 4, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 5, 1, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 1, 5, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 5, 2, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 1, 4, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 2, 5, 1, 3], [1, 1, 0, 1]]} "Class ", 6084, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 1, 4, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 5, 1, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 1, 5, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 5, 2, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 1, 4, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[4, 2, 5, 1, 3], [1, 0, 1, 1]]} "Class ", 6085, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 1, 4, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 5, 1, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 1, 5, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 5, 2, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 1, 4, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 2, 5, 1, 3], [1, 1, 1, 1]]} "Class ", 6086, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 1, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 5, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 5, 2], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 1, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 5, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 5, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 834, 3880, 19540, 105718, 610642, 3745718, 24290970, 165899600, 1189288863, 8922780578, 69881227339, 569991192811, 4832000010095, 42494151261208] "" "Class ", 6087, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 1, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 5, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 5, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 1, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 5, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 5, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 802, 3623, 17653, 92189, 513301, 3033553, 18954861, 124789946, 862961693, 6251100213, 47314277068, 373352221430, 3065106079087, 26131283750382] "" "Class ", 6088, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 1, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 5, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 5, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 5, 4, 1, 3], [0, 1, 0, 0]]} "Class ", 6089, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 1, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 5, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 5, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 5, 4, 1, 3], [1, 1, 0, 0]]} "Class ", 6090, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 1, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 5, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 5, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[2, 5, 4, 1, 3], [0, 0, 1, 0]]} "Class ", 6091, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 1, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 5, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 5, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[2, 5, 4, 1, 3], [1, 0, 1, 0]]} "Class ", 6092, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 1, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 5, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 5, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 5, 4, 1, 3], [0, 1, 1, 0]]} "Class ", 6093, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 1, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 5, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 5, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 5, 4, 1, 3], [1, 1, 1, 0]]} "Class ", 6094, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 1, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 5, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 5, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 1, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 5, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 5, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 824, 3802, 18975, 101669, 581281, 3528161, 22634908, 152912577, 1084225040, 8045584570, 62323318100, 502817692389, 4216486824800, 36683478703992] "" "Class ", 6095, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 1, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 5, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 5, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 1, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 5, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 5, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 790, 3520, 16874, 86587, 473589, 2750706, 16908624, 109655835, 748075302, 5353841370, 40095136181, 313475854231, 2553060013833, 21616990656046] "" "Class ", 6096, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 1, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 5, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 5, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 5, 4, 1, 3], [0, 1, 0, 1]]} "Class ", 6097, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 1, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 5, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 5, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 1, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 5, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 5, 2], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {4}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {4}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {4}, {}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2}, {[0, 0, 0, 1, 0, 0]}], [[3, 5, 1, 2, 4], {4}, {}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 5, 1, 2, 3], {4}, {}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 730, 2933, 12061, 50423, 213423, 912157, 3929637, 17043632, 74355634, 326071280, 1436553788, 6355447765, 28224026753, 125775609509] "" "Class ", 6098, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 1, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 5, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 5, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[2, 5, 4, 1, 3], [0, 0, 1, 1]]} "Class ", 6099, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 1, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 5, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 5, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[2, 5, 4, 1, 3], [1, 0, 1, 1]]} "Class ", 6100, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 1, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 5, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 5, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 5, 4, 1, 3], [0, 1, 1, 1]]} "Class ", 6101, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 1, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 5, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 5, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 2, 1, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 5, 4, 1, 3], [1, 1, 1, 1]]} "Class ", 6102, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 1, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 5, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 2, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 1, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 5, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 2, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[2, 4, 1, 3, 5], {1, 2}, {}], [[2, 5, 1, 3, 4], {1, 2}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 807, 3689, 18256, 97083, 551388, 3327041, 21232526, 142764553, 1008000774, 7451529172, 57523248541, 462644394095, 3868596436795, 33569642952504] "" "Class ", 6103, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 1, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 5, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 2, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 1, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 5, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 2, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {[1, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 780, 3451, 16428, 83604, 452510, 2594015, 15691993, 99843646, 666235800, 4650224508, 33872787205, 256949229422, 2025970883455, 16574938856893] "" "Class ", 6104, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 1, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 5, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 2, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 2, 4, 1, 3], [0, 1, 0, 0]]} "Class ", 6105, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 1, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 5, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 2, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 2, 4, 1, 3], [1, 1, 0, 0]]} "Class ", 6106, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 1, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 5, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 2, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[5, 2, 4, 1, 3], [0, 0, 1, 0]]} "Class ", 6107, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 1, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 5, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 2, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[5, 2, 4, 1, 3], [1, 0, 1, 0]]} "Class ", 6108, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 1, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 5, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 2, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 2, 4, 1, 3], [0, 1, 1, 0]]} "Class ", 6109, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 1, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 5, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 2, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 2, 4, 1, 3], [1, 1, 1, 0]]} "Class ", 6110, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 1, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 5, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 2, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 1, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 5, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 2, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[2, 4, 1, 3, 5], {1, 2, 4}, {}], [[2, 5, 1, 3, 4], {1, 2, 4}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 794, 3575, 17370, 90465, 502361, 2960475, 18438046, 120926064, 832555209, 6000411082, 45158489989, 354091882583, 2886914319531, 24428575330008] "" "Class ", 6111, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 1, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 5, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 2, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 1, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 5, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 2, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {[1, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 764, 3289, 15061, 72934, 371636, 1984435, 11067131, 64282626, 387932953, 2427121093, 15713307227, 105085735926, 724862207712, 5149957029353] "" "Class ", 6112, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 1, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 5, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 2, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 2, 4, 1, 3], [0, 1, 0, 1]]} "Class ", 6113, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 1, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 5, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 2, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 2, 4, 1, 3], [1, 1, 0, 1]]} "Class ", 6114, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 1, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 5, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 2, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[5, 2, 4, 1, 3], [0, 0, 1, 1]]} "Class ", 6115, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 1, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 5, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 2, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[5, 2, 4, 1, 3], [1, 0, 1, 1]]} "Class ", 6116, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 1, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 5, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 2, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 2, 4, 1, 3], [0, 1, 1, 1]]} "Class ", 6117, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 1, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 5, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 4, 2, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 2, 4, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 2, 4, 1, 3], [1, 1, 1, 1]]} "Class ", 6118, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 4, 1, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 2, 1, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 4, 5, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 2, 5, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 4, 1, 2], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[4, 5, 2, 1, 3], [0, 0, 1, 0]]} "Class ", 6119, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 4, 1, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 2, 1, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 4, 5, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 2, 5, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 4, 1, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[4, 5, 2, 1, 3], [1, 0, 1, 0]]} "Class ", 6120, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 4, 1, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 2, 5, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 4, 1, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 1, 0]]} "Class ", 6121, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 4, 1, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 2, 1, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 2, 5, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 4, 1, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 5, 2, 1, 3], [1, 1, 1, 0]]} "Class ", 6122, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 4, 1, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 2, 1, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 4, 5, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 2, 5, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 4, 1, 2], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[4, 5, 2, 1, 3], [0, 0, 1, 1]]} "Class ", 6123, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 4, 1, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 2, 1, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 4, 5, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 2, 5, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 4, 1, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[4, 5, 2, 1, 3], [1, 0, 1, 1]]} "Class ", 6124, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 4, 1, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 4, 5, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 2, 5, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 4, 1, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]} "Class ", 6125, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 4, 1, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 2, 1, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 4, 5, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 2, 5, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 4, 1, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 5, 2, 1, 3], [1, 1, 1, 1]]} "Class ", 6126, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 4, 2, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 2, 1, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 4, 5, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 2, 4, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 4, 2, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[5, 4, 2, 1, 3], [0, 0, 1, 0]]} "Class ", 6127, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 4, 2, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 2, 1, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 4, 5, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 2, 4, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 4, 2, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[5, 4, 2, 1, 3], [1, 0, 1, 0]]} "Class ", 6128, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 4, 2, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 2, 4, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 4, 2, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 1, 0]]} "Class ", 6129, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 4, 2, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 2, 4, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 4, 2, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 1, 0]]} "Class ", 6130, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 4, 2, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 2, 1, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 4, 5, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 2, 4, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 4, 2, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[5, 4, 2, 1, 3], [0, 0, 1, 1]]} "Class ", 6131, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 4, 2, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 2, 1, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 4, 5, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 2, 4, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 4, 2, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[5, 4, 2, 1, 3], [1, 0, 1, 1]]} "Class ", 6132, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 4, 2, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 4, 5, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 2, 4, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 4, 2, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 4, 2, 1, 3], [0, 1, 1, 1]]} "Class ", 6133, " is:" {{[[1, 3, 2], [1, 0]], [[3, 5, 4, 2, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 4, 5, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 1, 2, 4, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 5, 4, 2, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 4, 2, 1, 3], [1, 1, 1, 1]]} "Class ", 6134, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 4, 3, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 4, 3, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 3, 4}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 833, 3861, 19350, 103995, 595782, 3619827, 23221230, 156697234, 1108682552, 8201473935, 63274801039, 507991854586, 4235489216803, 36609247599146] "" "Class ", 6135, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 4, 3, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 4, 3, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {1, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 811, 3682, 17984, 93781, 518983, 3032488, 18629688, 119893166, 805753512, 5639525225, 41008440588, 309152095538, 2411668880931, 19434475797510] "" "Class ", 6136, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 2, 1, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 4, 3, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [0, 1, 0, 0]]} "Class ", 6137, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 4, 3, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 0, 0]]} "Class ", 6138, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 2, 1, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 4, 3, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [0, 0, 1, 0]]} "Class ", 6139, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 4, 3, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 1, 0]]} "Class ", 6140, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 2, 1, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 4, 3, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [0, 1, 1, 0]]} "Class ", 6141, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 4, 3, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 1, 0]]} "Class ", 6142, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 4, 3, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 4, 3, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {1}, {[0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 789, 3495, 16545, 83142, 441009, 2457963, 14339835, 87281820, 552702609, 3632275683, 24719681601, 173880087210, 1261984254525, 9435921363783] "" "Class ", 6143, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 4, 3, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 4, 3, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {1}, {[0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 773, 3336, 15207, 72697, 362447, 1876392, 10051083, 55544661, 315899245, 1845139684, 11048651523, 67719859612, 424287619507, 2714074517843] "" "Class ", 6144, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 2, 1, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 4, 3, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [0, 1, 0, 1]]} "Class ", 6145, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 4, 3, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 0, 1]]} "Class ", 6146, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 2, 1, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 4, 3, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 2, 1, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 4, 3, 1], [1, 1, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {1}, {[0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 789, 3495, 16545, 83142, 441009, 2457963, 14339835, 87281820, 552702609, 3632275683, 24719681601, 173880087210, 1261984254525, 9435921363783] "" "Class ", 6147, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 4, 3, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 2, 1, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 4, 3, 1], [1, 1, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {1}, {[0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 773, 3336, 15207, 72697, 362447, 1876392, 10051083, 55544661, 315899245, 1845139684, 11048651523, 67719859612, 424287619507, 2714074517843] "" "Class ", 6148, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 2, 1, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 4, 3, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [0, 1, 1, 1]]} "Class ", 6149, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 2, 1, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 4, 3, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 2, 3, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 3, 4, 5, 2], [1, 1, 1, 1]]} "Class ", 6150, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 2, 5, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 4, 5, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 2, 1, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 4, 1, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 2, 5, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 1, 2, 5, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 4, 5, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 2, 1, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 4, 1, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 1, 2, 5, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 3}, {[0, 0, 1, 0, 0]}], [[4, 1, 2, 3], {1, 3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 864, 4022, 20193, 108531, 620685, 3758437, 23997450, 160992186, 1131333280, 8305289619, 63543033058, 505607791619, 4176093376553, 35743340884895] "" "Class ", 6151, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 2, 5, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 4, 5, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 2, 1, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 4, 1, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 2, 5, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 1, 4, 5, 2], [1, 1, 0, 0]]} "Class ", 6152, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 2, 5, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 4, 5, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 2, 1, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 4, 1, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 2, 5, 3], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[3, 1, 4, 5, 2], [1, 0, 1, 0]]} "Class ", 6153, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 2, 5, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 4, 5, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 2, 1, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 4, 1, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 2, 5, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 1, 4, 5, 2], [1, 1, 1, 0]]} "Class ", 6154, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 2, 5, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 4, 5, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 2, 1, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 4, 1, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 2, 5, 3], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 1]], [[3, 1, 4, 5, 2], [1, 0, 0, 1]]} "Class ", 6155, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 2, 5, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 4, 5, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 2, 1, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 4, 1, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 2, 5, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 1, 4, 5, 2], [1, 1, 0, 1]]} "Class ", 6156, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 2, 5, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 4, 5, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 2, 1, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 4, 1, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 2, 5, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[3, 1, 4, 5, 2], [1, 0, 1, 1]]} "Class ", 6157, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 2, 5, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 4, 5, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 2, 1, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 4, 1, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 2, 5, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 1, 4, 5, 2], [1, 1, 1, 1]]} "Class ", 6158, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 3, 2, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 3, 5, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 3, 1, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 3, 4, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 3, 2, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 4, 3, 5, 2], [0, 1, 0, 0]]} "Class ", 6159, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 3, 2, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 3, 1, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 3, 4, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 3, 2, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 0, 0]]} "Class ", 6160, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 3, 2, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 3, 5, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 3, 1, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 3, 4, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 3, 2, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 4, 3, 5, 2], [0, 1, 1, 0]]} "Class ", 6161, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 3, 2, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 3, 1, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 3, 4, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 3, 2, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 1, 0]]} "Class ", 6162, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 3, 2, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 3, 5, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 3, 1, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 3, 4, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 3, 2, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 4, 3, 5, 2], [0, 1, 0, 1]]} "Class ", 6163, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 3, 2, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 3, 1, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 3, 4, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 3, 2, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 0, 1]]} "Class ", 6164, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 3, 2, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 3, 5, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 3, 1, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 3, 4, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 3, 2, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 4, 3, 5, 2], [0, 1, 1, 1]]} "Class ", 6165, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 3, 2, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 3, 1, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 3, 4, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 3, 2, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 4, 3, 5, 2], [1, 1, 1, 1]]} "Class ", 6166, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 3, 5, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 3, 5, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 3, 1, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 3, 1, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 3, 5, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 1, 3, 5, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 3, 5, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 3, 1, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 3, 1, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 1, 3, 5, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {1, 3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 864, 4022, 20193, 108531, 620685, 3758437, 23997450, 160992186, 1131333280, 8305289619, 63543033058, 505607791619, 4176093376553, 35743340884895] "" "Class ", 6167, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 3, 5, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 3, 5, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 3, 1, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 3, 1, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 3, 5, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 1, 3, 5, 2], [1, 1, 0, 0]]} "Class ", 6168, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 3, 5, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 3, 5, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 3, 1, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 3, 1, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 3, 5, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[4, 1, 3, 5, 2], [1, 0, 1, 0]]} "Class ", 6169, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 3, 5, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 3, 5, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 3, 1, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 3, 1, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 3, 5, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 1, 3, 5, 2], [1, 1, 1, 0]]} "Class ", 6170, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 3, 5, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 3, 5, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 3, 1, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 3, 1, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 3, 5, 2], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 1]], [[4, 1, 3, 5, 2], [1, 0, 0, 1]]} "Class ", 6171, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 3, 5, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 3, 5, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 3, 1, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 3, 1, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 3, 5, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 1, 3, 5, 2], [1, 1, 0, 1]]} "Class ", 6172, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 3, 5, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 3, 5, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 3, 1, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 3, 1, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 3, 5, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[4, 1, 3, 5, 2], [1, 0, 1, 1]]} "Class ", 6173, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 3, 5, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 3, 5, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 3, 1, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 3, 1, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 3, 5, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 1, 3, 5, 2], [1, 1, 1, 1]]} "Class ", 6174, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 5, 2, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 1, 5, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 5, 1, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 1, 4, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 5, 2, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 4, 1, 5, 2], [0, 1, 0, 0]]} "Class ", 6175, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 5, 2, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 1, 5, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 5, 1, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 1, 4, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 5, 2, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 4, 1, 5, 2], [1, 1, 0, 0]]} "Class ", 6176, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 5, 2, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 1, 5, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 5, 1, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 1, 4, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 5, 2, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 4, 1, 5, 2], [0, 1, 1, 0]]} "Class ", 6177, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 5, 2, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 1, 5, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 5, 1, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 1, 4, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 5, 2, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 4, 1, 5, 2], [1, 1, 1, 0]]} "Class ", 6178, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 5, 2, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 1, 5, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 5, 1, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 1, 4, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 5, 2, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 4, 1, 5, 2], [0, 1, 0, 1]]} "Class ", 6179, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 5, 2, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 1, 5, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 5, 1, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 1, 4, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 5, 2, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 4, 1, 5, 2], [1, 1, 0, 1]]} "Class ", 6180, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 5, 2, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 1, 5, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 5, 1, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 1, 4, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 5, 2, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 4, 1, 5, 2], [0, 1, 1, 1]]} "Class ", 6181, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 5, 2, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 1, 5, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 5, 1, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 1, 4, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 5, 2, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 4, 1, 5, 2], [1, 1, 1, 1]]} "Class ", 6182, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 5, 3, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 3, 1, 5, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 5, 1, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 1, 3, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 5, 3, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 3, 1, 5, 2], [1, 1, 0, 0]]} "Class ", 6183, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 5, 3, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 3, 1, 5, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 5, 1, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 1, 3, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 5, 3, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 3, 1, 5, 2], [1, 1, 1, 0]]} "Class ", 6184, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 5, 3, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 3, 1, 5, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 5, 1, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 1, 3, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 5, 3, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 3, 1, 5, 2], [1, 1, 0, 1]]} "Class ", 6185, " is:" {{[[1, 3, 2], [1, 0]], [[4, 1, 5, 3, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 3, 1, 5, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 5, 1, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 5, 1, 3, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 1, 5, 3, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 3, 1, 5, 2], [1, 1, 1, 1]]} "Class ", 6186, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 1, 3, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 4, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 2, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 5, 3, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 1, 3, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 1, 3, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 4, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 2, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 5, 3, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 2, 1, 3, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}], [[4, 2, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 3, 4], {1, 2, 4}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 197, 843, 3942, 19962, 108594, 630634, 3888596, 25344691, 173935091, 1252689685, 9440313292, 74249782683, 608097359487, 5175208422309, 45683099863021] "" "Class ", 6187, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 1, 3, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 4, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 2, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 5, 3, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 1, 3, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 1, 3, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 4, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 2, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 5, 3, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 2, 1, 3, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 823, 3790, 18871, 100852, 575040, 3480379, 22263081, 149950986, 1059993156, 7841553392, 60554175001, 487018733330, 4071215749086, 35308767782610] "" "Class ", 6188, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 1, 3, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 4, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 2, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 5, 3, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 1, 3, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 3, 5, 4, 2], [0, 1, 0, 0]]} "Class ", 6189, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 1, 3, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 2, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 5, 3, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 1, 3, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 0, 0]]} "Class ", 6190, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 1, 3, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 4, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 2, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 5, 3, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 1, 3, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 3, 5, 4, 2], [0, 0, 1, 0]]} "Class ", 6191, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 1, 3, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 4, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 2, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 5, 3, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 1, 3, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 3, 5, 4, 2], [1, 0, 1, 0]]} "Class ", 6192, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 1, 3, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 4, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 2, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 5, 3, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 1, 3, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 3, 5, 4, 2], [0, 1, 1, 0]]} "Class ", 6193, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 1, 3, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 2, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 5, 3, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 1, 3, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 1, 0]]} "Class ", 6194, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 1, 3, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 4, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 2, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 5, 3, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 1, 3, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 3, 5, 4, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 1, 3, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 4, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 2, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 5, 3, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 3, 5, 4, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 813, 3708, 18254, 96324, 541689, 3230758, 20351871, 134925540, 938453165, 6829022721, 51863722538, 410176883850, 3371468522443, 28749274772239] "" "Class ", 6195, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 1, 3, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 4, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 5, 3, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 1, 3, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 3, 5, 4, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 1, 3, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 4, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 5, 3, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 3, 5, 4, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 789, 3502, 16668, 84610, 456060, 2600755, 15641946, 98943068, 656580640, 4560329373, 33081415173, 250145673041, 1967997933873, 16081849997300] "" "Class ", 6196, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 1, 3, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 4, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 2, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 5, 3, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 1, 3, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 3, 5, 4, 2], [0, 1, 0, 1]]} "Class ", 6197, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 1, 3, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 2, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 5, 3, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 1, 3, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 0, 1]]} "Class ", 6198, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 1, 3, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 4, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 2, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 5, 3, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 1, 3, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 3, 5, 4, 2], [0, 0, 1, 1]]} "Class ", 6199, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 1, 3, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 4, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 2, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 5, 3, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 1, 3, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 3, 5, 4, 2], [1, 0, 1, 1]]} "Class ", 6200, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 1, 3, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 4, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 2, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 5, 3, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 1, 3, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 3, 5, 4, 2], [0, 1, 1, 1]]} "Class ", 6201, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 1, 3, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 3, 1, 2, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 5, 3, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 1, 3, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 3, 5, 4, 2], [1, 1, 1, 1]]} "Class ", 6202, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 1, 5, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 5, 4, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 1, 2, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 5, 1, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 1, 5, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 1, 5, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 5, 4, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 1, 2, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 5, 1, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 2, 1, 5, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {[0, 0, 1, 0, 0]}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 865, 4039, 20383, 110361, 637273, 3905197, 25288663, 172415549, 1233664141, 9237503126, 72202653113, 587775033471, 4973301802280, 43657061515022] "" "Class ", 6203, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 1, 5, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 5, 4, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 1, 2, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 5, 1, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 1, 5, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 1, 5, 4, 2], [1, 1, 0, 0]]} "Class ", 6204, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 1, 5, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 5, 4, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 1, 2, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 5, 1, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 1, 5, 3], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[3, 1, 5, 4, 2], [1, 0, 1, 0]]} "Class ", 6205, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 1, 5, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 5, 4, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 1, 2, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 5, 1, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 1, 5, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 1, 5, 4, 2], [1, 1, 1, 0]]} "Class ", 6206, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 1, 5, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 5, 4, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 1, 2, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 5, 1, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 1, 5, 3], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 1]], [[3, 1, 5, 4, 2], [1, 0, 0, 1]]} "Class ", 6207, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 1, 5, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 5, 4, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 1, 2, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 5, 1, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 1, 5, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 1, 5, 4, 2], [1, 1, 0, 1]]} "Class ", 6208, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 1, 5, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 5, 4, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 1, 2, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 5, 1, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 1, 5, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[3, 1, 5, 4, 2], [1, 0, 1, 1]]} "Class ", 6209, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 1, 5, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 5, 4, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 5, 1, 2, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 5, 1, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 1, 5, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 1, 5, 4, 2], [1, 1, 1, 1]]} "Class ", 6210, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 3, 2, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 5, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 3, 2, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 5, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {1, 3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {}], [[4, 2, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3}, {}], [[5, 2, 4, 1, 3], {1, 2}, {}], [[5, 3, 4, 1, 2], {1, 2}, {}], [[5, 3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 197, 843, 3942, 19962, 108594, 630634, 3888596, 25344691, 173935091, 1252689685, 9440313292, 74249782683, 608097359487, 5175208422309, 45683099863021] "" "Class ", 6211, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 3, 2, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 5, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 3, 2, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 5, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {1, 3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 805, 3658, 17938, 94285, 528208, 3138430, 19694080, 130050083, 900882283, 6528277261, 49366334918, 388695352878, 3180352378618, 26993079121440] "" "Class ", 6212, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 3, 2, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 5, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 1, 0, 0]]} "Class ", 6213, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 5, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 5, 1], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 1, 2, 4, 5], {4}, {}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 3, 5, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 764, 3292, 15121, 73673, 379000, 2050286, 11623261, 68845552, 424918013, 2726348422, 18145586756, 125034623262, 890421804041, 6542985431411] "" "Class ", 6214, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 3, 2, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 5, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 0, 1, 0]]} "Class ", 6215, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 3, 2, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 5, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 1, 0]]} "Class ", 6216, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 3, 2, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 5, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 1, 1, 0]]} "Class ", 6217, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 5, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 1, 0]]} "Class ", 6218, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 3, 2, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 5, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 3, 2, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 5, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 813, 3710, 18280, 96574, 543852, 3248719, 20499326, 136141440, 948615764, 6915581089, 52617413549, 416898513059, 3432931278745, 29325817455241] "" "Class ", 6219, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 3, 2, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 5, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 3, 2, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 5, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 763, 3270, 14844, 70961, 355673, 1862785, 10165879, 57673186, 339443431, 2068967527, 13039101751, 84846212977, 569306441734, 3934345877165] "" "Class ", 6220, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 3, 2, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 5, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 1, 0, 1]]} "Class ", 6221, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 5, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 5, 1], [1, 0, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {4}, {[0, 0, 0, 0, 0, 1]}], [[3, 5, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 5, 1, 2, 3], {4}, {[0, 0, 0, 0, 0, 1]}], [[4, 5, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 731, 2950, 12235, 51822, 223191, 974427, 4302645, 19181100, 86211885, 390248055, 1777495635, 8140539950, 37463689775, 173164232965] "" "Class ", 6222, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 3, 2, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 5, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 3, 2, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 5, 1], [1, 1, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 813, 3710, 18280, 96574, 543852, 3248719, 20499326, 136141440, 948615764, 6915581089, 52617413549, 416898513059, 3432931278745, 29325817455241] "" "Class ", 6223, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 3, 2, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 5, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 3, 2, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 5, 1], [1, 1, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 763, 3270, 14844, 70961, 355673, 1862785, 10165879, 57673186, 339443431, 2068967527, 13039101751, 84846212977, 569306441734, 3934345877165] "" "Class ", 6224, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 3, 2, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 5, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [0, 1, 1, 1]]} "Class ", 6225, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 5, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 3, 2, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 5, 1], [1, 1, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 5, 3, 4, 2], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {4}, {[0, 0, 0, 0, 0, 1]}], [[3, 5, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 5, 1, 2, 3], {4}, {[0, 0, 0, 0, 0, 1]}], [[4, 5, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 731, 2950, 12235, 51822, 223191, 974427, 4302645, 19181100, 86211885, 390248055, 1777495635, 8140539950, 37463689775, 173164232965] "" "Class ", 6226, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 3, 2, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 3, 2, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {}, {}], [[4, 1, 2, 3], {1, 3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}], [[3, 1, 2, 4, 5], {1, 3, 4}, {}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 3, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 806, 3681, 18209, 96785, 549236, 3310121, 21091197, 141530421, 996876401, 7348714755, 56551248933, 453250158751, 3775779765928, 32632064665091] "" "Class ", 6227, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 3, 2, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 3, 2, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 3}, {[1, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 793, 3567, 17337, 90403, 502788, 2967988, 18516923, 121640308, 838619812, 6050451896, 45566632005, 357405491313, 2913725824843, 24644119350993] "" "Class ", 6228, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 3, 2, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 3, 2, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1, 5], [0, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {}, {[0, 0, 0, 0, 1]}], [[4, 1, 3, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {3}, {[0, 0, 0, 0, 0, 1]}], [[5, 1, 2, 4, 3], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 764, 3290, 15084, 73252, 375111, 2017811, 11364679, 66824497, 409158205, 2602605156, 17162079982, 117097991373, 825279396020, 5998604320203] "" "Class ", 6229, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1, 5], [0, 0, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {}, {[0, 0, 0, 0, 1]}], [[4, 1, 3, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {3}, {[0, 0, 0, 0, 0, 1]}], [[5, 1, 2, 4, 3], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 764, 3290, 15084, 73252, 375111, 2017811, 11364679, 66824497, 409158205, 2602605156, 17162079982, 117097991373, 825279396020, 5998604320203] "" "Class ", 6230, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 3, 2, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [0, 0, 1, 0]]} "Class ", 6231, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 3, 2, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [1, 0, 1, 0]]} "Class ", 6232, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 3, 2, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [0, 1, 1, 0]]} "Class ", 6233, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 1, 0]]} "Class ", 6234, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 3, 2, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 3, 2, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 762, 3257, 14734, 70164, 350173, 1824916, 9900831, 55776020, 325541041, 1964740513, 12240641505, 78603636042, 519551554402, 3530432003317] "" "Class ", 6235, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 3, 2, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 3, 2, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 747, 3111, 13551, 61419, 288543, 1400727, 7008519, 36065919, 190531623, 1031674935, 5717624727, 32392623783, 187392817623, 1105868383095] "" "Class ", 6236, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 3, 2, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 3, 2, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 731, 2950, 12235, 51822, 223191, 974427, 4302645, 19181100, 86211885, 390248055, 1777495635, 8140539950, 37463689775, 173164232965] "" "Class ", 6237, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1, 5], [1, 0, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 731, 2950, 12235, 51822, 223191, 974427, 4302645, 19181100, 86211885, 390248055, 1777495635, 8140539950, 37463689775, 173164232965] "" "Class ", 6238, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 3, 2, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 3, 2, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1, 5], [1, 1, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 762, 3257, 14734, 70164, 350173, 1824916, 9900831, 55776020, 325541041, 1964740513, 12240641505, 78603636042, 519551554402, 3530432003317] "" "Class ", 6239, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 3, 2, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 3, 2, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1, 5], [1, 1, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 747, 3111, 13551, 61419, 288543, 1400727, 7008519, 36065919, 190531623, 1031674935, 5717624727, 32392623783, 187392817623, 1105868383095] "" "Class ", 6240, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 3, 2, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 3, 2, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1, 5], [1, 1, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 731, 2950, 12235, 51822, 223191, 974427, 4302645, 19181100, 86211885, 390248055, 1777495635, 8140539950, 37463689775, 173164232965] "" "Class ", 6241, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 5, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 3, 2, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1, 5], [1, 1, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 1, 3, 4, 2], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 731, 2950, 12235, 51822, 223191, 974427, 4302645, 19181100, 86211885, 390248055, 1777495635, 8140539950, 37463689775, 173164232965] "" "Class ", 6242, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 2, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 1, 5, 3], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 2, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 1, 5, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {}], [[3, 2, 4, 1, 5], {1, 2}, {}], [[3, 2, 5, 1, 4], {1, 2, 3}, {}], [[4, 2, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 1, 2], {1, 2, 3}, {}], [[4, 3, 5, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 826, 3824, 19166, 103203, 593222, 3620806, 23362266, 158736875, 1132000731, 8448021142, 65808789817, 533872701725, 4501159156894, 39367690046924] "" "Class ", 6243, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 4, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 2, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 1, 5, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 4, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 2, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 1, 5, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 804, 3646, 17847, 93686, 524501, 3117009, 19583796, 129624283, 901045384, 6559437238, 49883837162, 395409226246, 3260167446538, 27908205583731] "" "Class ", 6244, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 2, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 1, 5, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 1, 0, 0]]} "Class ", 6245, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 4, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 2, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 1, 5, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 4, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 2, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 1, 5, 3], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 791, 3530, 16928, 86710, 472118, 2721105, 16542806, 105755071, 708978461, 4972092924, 36396332778, 277532143421, 2200421394355, 18109227996017] "" "Class ", 6246, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 2, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 1, 5, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 0, 1, 0]]} "Class ", 6247, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 4, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 2, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 1, 5, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[3, 5, 1, 4, 2], [1, 0, 1, 0]]} "Class ", 6248, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 2, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 1, 5, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 1, 1, 0]]} "Class ", 6249, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 4, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 2, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 1, 5, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 5, 1, 4, 2], [1, 1, 1, 0]]} "Class ", 6250, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 2, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 1, 5, 3], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 2, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 1, 5, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 791, 3534, 16991, 87353, 477745, 2767385, 16913676, 108703811, 732501031, 5161689661, 37947088506, 290436666315, 2309837400799, 19055243556947] "" "Class ", 6251, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 4, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 2, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 1, 5, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 1]], [[3, 5, 1, 4, 2], [1, 0, 0, 1]]} "Class ", 6252, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 2, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 1, 5, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 1, 0, 1]]} "Class ", 6253, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 4, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 2, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 1, 5, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 5, 1, 4, 2], [1, 1, 0, 1]]} "Class ", 6254, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 2, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 1, 5, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 0, 1, 1]]} "Class ", 6255, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 4, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 2, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 1, 5, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[3, 5, 1, 4, 2], [1, 0, 1, 1]]} "Class ", 6256, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 2, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 1, 5, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 5, 1, 4, 2], [0, 1, 1, 1]]} "Class ", 6257, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 1, 4, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 5, 2, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 1, 5, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 5, 1, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 5, 1, 4, 2], [1, 1, 1, 1]]} "Class ", 6258, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 5, 3, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 1, 4, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 5, 2, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 1, 3, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 5, 3, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 3, 1, 4, 2], [0, 1, 0, 0]]} "Class ", 6259, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 5, 3, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 1, 4, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 1, 3, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 5, 3, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 3, 1, 4, 2], [1, 1, 0, 0]]} "Class ", 6260, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 5, 3, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 1, 4, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 5, 2, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 1, 3, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 5, 3, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 3, 1, 4, 2], [0, 1, 1, 0]]} "Class ", 6261, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 5, 3, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 1, 4, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 1, 3, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 5, 3, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 3, 1, 4, 2], [1, 1, 1, 0]]} "Class ", 6262, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 5, 3, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 1, 4, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 5, 2, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 1, 3, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 5, 3, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 3, 1, 4, 2], [0, 1, 0, 1]]} "Class ", 6263, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 5, 3, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 1, 4, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 1, 3, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 5, 3, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 3, 1, 4, 2], [1, 1, 0, 1]]} "Class ", 6264, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 5, 3, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 1, 4, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 5, 2, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 1, 3, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 5, 3, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 3, 1, 4, 2], [0, 1, 1, 1]]} "Class ", 6265, " is:" {{[[1, 3, 2], [1, 0]], [[4, 2, 5, 3, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 1, 4, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 5, 2, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 4, 1, 3, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 2, 5, 3, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 3, 1, 4, 2], [1, 1, 1, 1]]} "Class ", 6266, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 1, 2, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 5, 4, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 1, 2, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 1, 2, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 5, 4, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 3, 1, 2, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {1}, {}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 4}, {}], [[5, 4, 1, 2, 3], {1, 2, 4}, {}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 198, 851, 3998, 20342, 111204, 648905, 4020080, 26322030, 181450140, 1312487393, 9932589184, 78440304879, 644956184005, 5509911051915, 48818053099749] "" "Class ", 6267, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 1, 2, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 5, 4, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 1, 2, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 1, 2, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 5, 4, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 3, 1, 2, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 825, 3816, 19123, 103053, 593449, 3632437, 23524108, 160549079, 1150756803, 8636272455, 67682462667, 552589105093, 4690114810050, 41303923261973] "" "Class ", 6268, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 1, 2, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 3, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 3, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 5, 4, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 1, 2, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 4, 5, 3, 2], [0, 1, 0, 0]]} "Class ", 6269, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 1, 2, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 5, 4, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 1, 2, 5], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 0, 0]]} "Class ", 6270, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 1, 2, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 3, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 3, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 5, 4, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 1, 2, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 4, 5, 3, 2], [0, 0, 1, 0]]} "Class ", 6271, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 1, 2, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 5, 4, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 1, 2, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 1, 0]]} "Class ", 6272, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 1, 2, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 3, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 3, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 5, 4, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 1, 2, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 4, 5, 3, 2], [0, 1, 1, 0]]} "Class ", 6273, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 1, 2, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 5, 4, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 1, 2, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 1, 0]]} "Class ", 6274, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 1, 2, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 3, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 3, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 5, 4, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 1, 2, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 4, 5, 3, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 1, 2, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 3, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 3, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 5, 4, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 4, 5, 3, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 822, 3774, 18714, 99485, 563572, 3385052, 21466658, 143206522, 1001797300, 7328308067, 55919392187, 444119676574, 3664020609364, 31344460836443] "" "Class ", 6275, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 1, 2, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 5, 4, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 1, 2, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 1, 2, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 5, 4, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 789, 3500, 16616, 83857, 447466, 2513177, 14799522, 91071981, 583951826, 3891570727, 26894248605, 192362538985, 1421479845253, 10835066678862] "" "Class ", 6276, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 1, 2, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 3, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 3, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 5, 4, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 1, 2, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 4, 5, 3, 2], [0, 1, 0, 1]]} "Class ", 6277, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 1, 2, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 5, 4, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 1, 2, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 0, 1]]} "Class ", 6278, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 1, 2, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 3, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 3, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 5, 4, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 1, 2, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 4, 5, 3, 2], [0, 0, 1, 1]]} "Class ", 6279, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 1, 2, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 3, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 5, 4, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 1, 2, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 4, 5, 3, 2], [1, 0, 1, 1]]} "Class ", 6280, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 1, 2, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 3, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 3, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 5, 4, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 1, 2, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 4, 5, 3, 2], [0, 1, 1, 1]]} "Class ", 6281, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 1, 2, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 2, 1, 3, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 5, 4, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 1, 2, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 4, 5, 3, 2], [1, 1, 1, 1]]} "Class ", 6282, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 1, 5, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 5, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 1, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 5, 1, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 1, 5, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 1, 5, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 5, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 1, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 5, 1, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 3, 1, 5, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 866, 4053, 20517, 111492, 646387, 3977676, 25867411, 177102454, 1272385479, 9564976111, 75043373479, 613078965929, 5204871181174, 45834613408314] "" "Class ", 6283, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 1, 5, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 5, 3, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 1, 3, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 5, 1, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 1, 5, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 1, 5, 3, 2], [1, 1, 0, 0]]} "Class ", 6284, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 1, 5, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 5, 3, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 1, 3, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 5, 1, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 1, 5, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[4, 1, 5, 3, 2], [1, 0, 1, 0]]} "Class ", 6285, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 1, 5, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 5, 3, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 1, 3, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 5, 1, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 1, 5, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 1, 5, 3, 2], [1, 1, 1, 0]]} "Class ", 6286, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 1, 5, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 5, 3, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 1, 3, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 5, 1, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 1, 5, 2], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 1]], [[4, 1, 5, 3, 2], [1, 0, 0, 1]]} "Class ", 6287, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 1, 5, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 5, 3, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 1, 3, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 5, 1, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 1, 5, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 1, 5, 3, 2], [1, 1, 0, 1]]} "Class ", 6288, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 1, 5, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 5, 3, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 1, 3, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 5, 1, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 1, 5, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[4, 1, 5, 3, 2], [1, 0, 1, 1]]} "Class ", 6289, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 1, 5, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 1, 5, 3, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 5, 1, 3, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 5, 1, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 1, 5, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 1, 5, 3, 2], [1, 1, 1, 1]]} "Class ", 6290, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {}, {}], [[4, 3, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 2, 3}, {}], [[5, 4, 2, 1, 3], {1, 2, 3}, {}], [[5, 4, 3, 1, 2], {1, 2, 3}, {}], [[5, 4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 198, 851, 3998, 20342, 111204, 648905, 4020080, 26322030, 181450140, 1312487393, 9932589184, 78440304879, 644956184005, 5509911051915, 48818053099749] "" "Class ", 6291, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 826, 3825, 19187, 103495, 596512, 3654001, 23679811, 161708286, 1159676180, 8707262073, 68266976145, 557566336939, 4733918011791, 41702038751134] "" "Class ", 6292, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 3, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 1, 0, 0]]} "Class ", 6293, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 5, 1], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {}, {}], [[4, 2, 1, 3], {}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1]}], [[3, 2, 1, 4, 5], {4}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 3, 5], {4}, {}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 2, 5], {4}, {}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 2, 1, 3, 4], {4}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {4}, {}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[5, 4, 1, 2, 3], {4}, {}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 780, 3453, 16478, 84314, 460379, 2671376, 16411050, 106377186, 725314285, 5187245750, 38810682669, 303065895353, 2464625082752, 20832007625375] "" "Class ", 6294, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 3, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 5, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 0, 1, 0]]} "Class ", 6295, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 5, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 0]]} "Class ", 6296, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 3, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 5, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 1, 1, 0]]} "Class ", 6297, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 5, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 0]]} "Class ", 6298, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 834, 3879, 19542, 105808, 611747, 3756737, 24393522, 166831473, 1197729400, 8999868845, 70595941456, 576744497923, 4897185279080, 43137752932269] "" "Class ", 6299, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 803, 3636, 17779, 93294, 522564, 3109748, 19579807, 129953824, 906236525, 6620524677, 50536065259, 402110249253, 3328143235321, 28598241845327] "" "Class ", 6300, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 3, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 1, 0, 1]]} "Class ", 6301, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 5, 1], [1, 0, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {4}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {4}, {[0, 0, 0, 0, 0, 1]}], [[3, 5, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 5, 1, 2, 3], {4}, {[0, 0, 0, 0, 0, 1]}], [[4, 5, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 749, 3145, 13915, 64626, 314200, 1595920, 8455356, 46661372, 267855591, 1597252545, 9880530031, 63316773521, 419747266919, 2874717861744] "" "Class ", 6302, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 3, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 5, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 0, 1, 1]]} "Class ", 6303, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 5, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 1]]} "Class ", 6304, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 3, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 5, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[1, 5, 4, 3, 2], [0, 1, 1, 1]]} "Class ", 6305, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 5, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]} "Class ", 6306, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 1, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 1, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}], [[3, 2, 1, 4, 5], {1, 2, 4}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 819, 3794, 19081, 103289, 597660, 3675642, 23912630, 163902600, 1179512133, 8885168211, 69875164296, 572337739776, 4872392851252, 43030180417817] "" "Class ", 6307, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 1, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 1, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {[1, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 807, 3696, 18372, 98335, 563015, 3428921, 22107366, 150270387, 1073070016, 8025303113, 62689692391, 510256957969, 4318263135347, 37924597070286] "" "Class ", 6308, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 3, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 1, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [0, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 3, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 1, 5], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [0, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {}, {}], [[4, 2, 1, 3], {}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {1}, {}], [[3, 2, 1, 4, 5], {4}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 3, 5], {4}, {}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 2, 5], {4}, {}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 3, 4], {4}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {4}, {}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {2, 3}, {}], [[5, 4, 1, 2, 3], {4}, {}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 779, 3438, 16335, 83184, 452188, 2614094, 16013603, 103595904, 705488939, 5042421027, 37722469371, 294636929003, 2397246062687, 20275884076527] "" "Class ", 6309, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 1, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 1, 5], [0, 0, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 0, 0, 1]}], [[4, 1, 3, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 1, 4, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 779, 3438, 16335, 83184, 452188, 2614094, 16013603, 103595904, 705488939, 5042421027, 37722469371, 294636929003, 2397246062687, 20275884076527] "" "Class ", 6310, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 3, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 1, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 0, 1, 0]]} "Class ", 6311, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 1, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 1, 0]]} "Class ", 6312, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 3, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 1, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 1, 1, 0]]} "Class ", 6313, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 1, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 1, 0]]} "Class ", 6314, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 3, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 1, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 3, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 1, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 793, 3571, 17418, 91401, 512791, 3059362, 19321121, 128656998, 900211748, 6598690410, 50537645153, 403445957848, 3350000505309, 28877580399076] "" "Class ", 6315, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 1, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 1, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 0, 0, 1]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 778, 3423, 16185, 81871, 441172, 2522430, 15246711, 97103259, 649654820, 4553427688, 33352574723, 254732113821, 2024501994289, 16711976124523] "" "Class ", 6316, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 3, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 1, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 3, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 1, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 0, 0, 1]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 748, 3129, 13756, 63335, 304693, 1529100, 7994528, 43492705, 245921947, 1443484678, 8784512496, 55354500443, 360701375532, 2427352813989] "" "Class ", 6317, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 1, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 1, 5], [1, 0, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 0, 0, 1]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 748, 3129, 13756, 63335, 304693, 1529100, 7994528, 43492705, 245921947, 1443484678, 8784512496, 55354500443, 360701375532, 2427352813989] "" "Class ", 6318, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 3, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 1, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 0, 1, 1]]} "Class ", 6319, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 3, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 1, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 0, 1, 1]]} "Class ", 6320, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 3, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 1, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [0, 1, 1, 1]]} "Class ", 6321, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 5, 2, 3, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 4, 1, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 2, 5, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 1, 4, 3, 2], [1, 1, 1, 1]]} "Class ", 6322, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 5, 4], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 5, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {}], [[3, 2, 4, 1, 5], {1, 2}, {}], [[3, 2, 5, 1, 4], {1, 2, 3}, {}], [[4, 2, 5, 1, 3], {1, 2, 3}, {}], [[4, 3, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 828, 3852, 19431, 105424, 611117, 3763904, 24516419, 168211436, 1211562651, 9133347312, 71872894292, 589030103174, 5016964825243, 44326265282635] "" "Class ", 6323, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 5, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 5, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 815, 3738, 18547, 98829, 562136, 3395645, 21688315, 145917961, 1030712644, 7621687923, 58847943484, 473347363401, 3958229609329, 34346715634636] "" "Class ", 6324, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 5, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 5, 4], [0, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 0, 1]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 790, 3518, 16830, 85991, 466971, 2684076, 16271021, 103703085, 692984332, 4843252797, 35323875932, 268314637330, 2118707663672, 17362893451423] "" "Class ", 6325, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 5, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 5, 4], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {[0, 1, 0, 0, 0]}], [[3, 2, 4, 1, 5], {1, 2}, {[0, 1, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 3}, {[0, 1, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {1, 3}, {[0, 1, 0, 0, 0, 0]}], [[4, 3, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 790, 3518, 16830, 85991, 466971, 2684076, 16271021, 103703085, 692984332, 4843252797, 35323875932, 268314637330, 2118707663672, 17362893451423] "" "Class ", 6326, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 3, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 5, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 0, 1, 0]]} "Class ", 6327, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 3, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 5, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [1, 0, 1, 0]]} "Class ", 6328, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 5, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 1, 0]]} "Class ", 6329, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 5, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 1, 0]]} "Class ", 6330, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 3, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 5, 4], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 3, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 5, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 789, 3505, 16701, 84788, 456051, 2586518, 15406249, 96043642, 624802529, 4230513882, 29745796687, 216748609085, 1633782708281, 12718258527147] "" "Class ", 6331, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 3, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 5, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [1, 0, 0, 1]]} "Class ", 6332, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 746, 3094, 13371, 59873, 276670, 1315254, 6416483, 32058125, 163752469, 853905967, 4539986433, 24583331287, 135439367666, 758561402406] "" "Class ", 6333, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 5, 4], [1, 0, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 746, 3094, 13371, 59873, 276670, 1315254, 6416483, 32058125, 163752469, 853905967, 4539986433, 24583331287, 135439367666, 758561402406] "" "Class ", 6334, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 3, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 5, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 0, 1, 1]]} "Class ", 6335, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 3, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 5, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [1, 0, 1, 1]]} "Class ", 6336, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 3, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 5, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [0, 1, 1, 1]]} "Class ", 6337, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 5, 3, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 5, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 5, 1, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 5, 1, 3, 2], [1, 1, 1, 1]]} "Class ", 6338, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {}], [[3, 2, 4, 1, 5], {1, 2}, {}], [[3, 2, 5, 1, 4], {1, 2, 3}, {}], [[4, 2, 5, 1, 3], {1, 2, 3}, {}], [[4, 3, 5, 1, 2], {1, 2, 3}, {}], [[4, 3, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 819, 3797, 19119, 103604, 599931, 3691531, 24025411, 164727202, 1185749499, 8934034461, 70271754671, 575670798388, 4901379650523, 43290806579867] "" "Class ", 6339, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 767, 3350, 15822, 80584, 440495, 2570122, 15922684, 104265857, 718841241, 5200295834, 39359924005, 310877931049, 2556456685395, 21842807645436] "" "Class ", 6340, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 0, 0]]} "Class ", 6341, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4, 5], [0, 0, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {2}, {[0, 0, 0, 1]}], [[3, 2, 1], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 750, 3169, 14245, 68135, 346706, 1874878, 10753923, 65257969, 417756892, 2812930320, 19865782643, 146761631811, 1131423565989, 9082099786423] "" "Class ", 6342, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 3, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 3, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4, 5], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}], [[3, 2, 4, 1, 5], {2, 3}, {}], [[3, 2, 5, 1, 4], {2, 3}, {}], [[4, 2, 5, 1, 3], {2, 3}, {}], [[4, 3, 5, 1, 2], {2, 3}, {}], [[4, 3, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 793, 3569, 17387, 91096, 510269, 3039876, 19173301, 127528713, 891439050, 6528769670, 49964541118, 398607640710, 3307903021497, 28500059185317] "" "Class ", 6343, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 3, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 3, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4, 5], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 732, 2970, 12474, 54058, 241355, 1109469, 5250168, 25579563, 128352204, 663513675, 3534736190, 19408720119, 109842347882, 640611673645] "" "Class ", 6344, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 1, 0]]} "Class ", 6345, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4, 5], [0, 1, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {2}, {[0, 0, 0, 1]}], [[3, 2, 1], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 732, 2970, 12474, 54058, 241355, 1109469, 5250168, 25579563, 128352204, 663513675, 3534736190, 19408720119, 109842347882, 640611673645] "" "Class ", 6346, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 3, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 3, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 0, 0, 1]}], [[3, 2, 1], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 793, 3569, 17383, 91017, 509294, 3029960, 19081023, 126702411, 884126858, 6463855134, 49381308424, 393276187707, 3258158169194, 28025395373787] "" "Class ", 6347, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 3, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 3, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {2}, {[0, 0, 0, 1]}], [[3, 2, 1], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}] , [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 733, 2990, 12711, 56245, 258841, 1237546, 6138785, 31547846, 167732789, 921434619, 5223792251, 30527332036, 183698380677, 1137081921786] "" "Class ", 6348, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 0, 0, 1]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [5, 3, 4, 1, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [ [5, 3, 4, 2, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 765, 3309, 15311, 75471, 394667, 2180854, 12687070, 77443458, 494547638, 3295275794, 22857305753, 164705084124, 1230636295559, 9518410705976] "" "Class ", 6349, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 0, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {2}, {[0, 0, 0, 1]}], [[3, 2, 1], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 187, 715, 2795, 11051, 43947, 175275, 700075, 2798251, 11188907, 44747435, 178973355, 715860651, 2863377067, 11453377195, 45813246635] "" "Class ", 6350, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 3, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 3, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 1, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 0, 0, 1]}], [[3, 2, 1], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 780, 3458, 16574, 85465, 471684, 2772266, 17272325, 113614207, 786185012, 5705008983, 43292685504, 342705147785, 2823643775457, 24166565128233] "" "Class ", 6351, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 3, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 3, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 1, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {2}, {[0, 0, 0, 1]}], [[3, 2, 1], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 187, 715, 2795, 11051, 43947, 175275, 700075, 2798251, 11188907, 44747435, 178973355, 715860651, 2863377067, 11453377195, 45813246635] "" "Class ", 6352, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 3, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]} "Class ", 6353, " is:" {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 5, 2, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 5, 3, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4, 5], [1, 1, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {2}, {[0, 0, 0, 1]}], [[3, 2, 1], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 187, 715, 2795, 11051, 43947, 175275, 700075, 2798251, 11188907, 44747435, 178973355, 715860651, 2863377067, 11453377195, 45813246635] "" "Class ", 6354, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 5, 4, 3], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 5, 4, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[3, 4, 1, 2, 5], {1, 2}, {}], [[3, 5, 1, 2, 4], {1, 2}, {}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 814, 3720, 18336, 96734, 542771, 3222375, 20155200, 132326060, 909000559, 6515288873, 48605629396, 376594908778, 3024472469864, 25133305134868] "" "Class ", 6355, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 5, 4, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 5, 4, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 800, 3587, 17244, 88240, 477814, 2724770, 16297426, 101890433, 663882227, 4496527557, 31587472619, 229688816211, 1725767673516, 13376793059522] "" "Class ", 6356, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 5, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 5, 4, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [0, 1, 0, 0]]} "Class ", 6357, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 5, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 5, 4, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [1, 1, 0, 0]]} "Class ", 6358, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {4}, {}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 2, 4], {4}, {}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {2, 3}, {}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 774, 3355, 15424, 74738, 379805, 2016080, 11141072, 63912803, 379692351, 2330980706, 14760433225, 96248864561, 645337609935, 4443205351133] "" "Class ", 6359, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {[0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {1, 2}, {[0, 0, 1, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 2, 4], {1, 2}, {[0, 0, 1, 0, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {2, 3}, {}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3, 4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 760, 3221, 14334, 66552, 320838, 1599983, 8228866, 43538843, 236490099, 1316333938, 7496486568, 43620779739, 259028416111, 1568019935835] "" "Class ", 6360, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 5, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 5, 4, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 5, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 5, 4, 3], [0, 1, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 2, 5, 4, 3], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 3, 5, 4, 2], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {4}, {[0, 0, 0, 0, 0, 1]}], [[2, 3, 5, 4, 1], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 4, 5, 1, 3], {4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 3, 1], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 774, 3355, 15424, 74738, 379805, 2016080, 11141072, 63912803, 379692351, 2330980706, 14760433225, 96248864561, 645337609935, 4443205351133] "" "Class ", 6361, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 5, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 5, 4, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [1, 1, 1, 0]]} "Class ", 6362, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 5, 4, 3], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 5, 4, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 789, 3498, 16593, 83664, 445971, 2502030, 14718189, 90486387, 579774807, 3862014909, 26687220198, 190936039110, 1411937246232, 10774765224822] "" "Class ", 6363, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 5, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 5, 4, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [1, 0, 0, 1]]} "Class ", 6364, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 5, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 5, 4, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [0, 1, 0, 1]]} "Class ", 6365, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 5, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 5, 4, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [1, 1, 0, 1]]} "Class ", 6366, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 5, 4, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 5, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 5, 4, 3], [1, 1, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 2, 5, 4, 3], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 3, 5, 4, 2], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}], [ [2, 3, 5, 4, 1], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {4}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}], [ [2, 4, 5, 3, 1], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 750, 3150, 13897, 64037, 306868, 1523862, 7818940, 41351272, 224934199, 1256192911, 7191170808, 42138057776, 252428284029, 1544200823492] "" "Class ", 6367, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 5, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 5, 4, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [1, 0, 1, 1]]} "Class ", 6368, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 5, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 5, 4, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 5, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 5, 4, 3], [1, 1, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 2, 5, 4, 3], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 3, 5, 4, 2], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}], [ [2, 3, 5, 4, 1], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {4}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}], [ [2, 4, 5, 3, 1], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 750, 3150, 13897, 64037, 306868, 1523862, 7818940, 41351272, 224934199, 1256192911, 7191170808, 42138057776, 252428284029, 1544200823492] "" "Class ", 6369, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 5, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 5, 4, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 1, 2, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 4, 5, 1, 2], [1, 1, 1, 1]]} "Class ", 6370, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 3, 5, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 5, 3, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 3, 5, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 5, 3, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 862, 3989, 19835, 105216, 591870, 3513124, 21910321, 143064559, 974996705, 6916676160, 50955676420, 389030085928, 3072287102037, 25055535604297] "" "Class ", 6371, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 1, 3, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 3, 5, 1, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1, 5, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 5, 3, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 1, 3, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 3, 5, 1, 2], [1, 1, 0, 0]]} "Class ", 6372, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 3, 5, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 3, 5, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 858, 3911, 18872, 95461, 502640, 2740784, 15416888, 89190280, 529412359, 3217881949, 19995243777, 126837869434, 820357014340, 5404050066627] "" "Class ", 6373, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 1, 3, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 3, 5, 1, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1, 5, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 5, 3, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 1, 3, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 3, 5, 1, 2], [1, 1, 1, 0]]} "Class ", 6374, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 1, 3, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 3, 5, 1, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1, 5, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 5, 3, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 1, 3, 2], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 1]], [[4, 3, 5, 1, 2], [1, 0, 0, 1]]} "Class ", 6375, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 1, 3, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 3, 5, 1, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1, 5, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 5, 3, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 1, 3, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 3, 5, 1, 2], [1, 1, 0, 1]]} "Class ", 6376, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 1, 3, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 3, 5, 1, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1, 5, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 5, 3, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 1, 3, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[4, 3, 5, 1, 2], [1, 0, 1, 1]]} "Class ", 6377, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 1, 3, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 3, 5, 1, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1, 5, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 5, 3, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 1, 3, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 3, 5, 1, 2], [1, 1, 1, 1]]} "Class ", 6378, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 5, 3], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 5, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 826, 3825, 19177, 103288, 593827, 3625077, 23392875, 158962080, 1133710669, 8461444464, 65917790349, 534788131993, 4509106492252, 39438957931254] "" "Class ", 6379, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 5, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 5, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 803, 3633, 17730, 92744, 517207, 3061013, 19150472, 126213483, 873597865, 6332941277, 47963954856, 378677791248, 3110200650945, 26525692173496] "" "Class ", 6380, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 5, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 5, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 1, 0, 0]]} "Class ", 6381, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 1, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 5, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 5, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 5, 4, 1, 2], [1, 1, 0, 0]]} "Class ", 6382, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {}, {}], [[2, 3, 1, 4, 5], {1, 2}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {4}, {}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 1, 5], {3}, {}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 2, 4], {4}, {}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {3}, {}], [[3, 5, 2, 4, 1], {2, 3}, {}], [[4, 5, 1, 2, 3], {4}, {}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3}, {}], [[4, 5, 3, 1, 2], {3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 791, 3535, 17017, 87718, 481711, 2805697, 17264523, 111849042, 760584597, 5413992981, 40242284739, 311664529960, 2509965148111, 20981572888461] "" "Class ", 6383, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {4}, {}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 2, 4], {4}, {}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {2, 3}, {}], [[4, 5, 1, 2, 3], {4}, {}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3, 4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 776, 3386, 15753, 77722, 404941, 2220254, 12773385, 76913539, 483641570, 3169557156, 21609068528, 153005717885, 1123408835738, 8540753556675] "" "Class ", 6384, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 5, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 5, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 1, 1, 0]]} "Class ", 6385, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 1, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 5, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 5, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 5, 4, 1, 2], [1, 1, 1, 0]]} "Class ", 6386, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 5, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 5, 3], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 5, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 5, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 815, 3738, 18550, 98869, 562506, 3398696, 21712546, 146109249, 1032236327, 7634029617, 58950039360, 474212037466, 3965736578725, 34413563231894] "" "Class ", 6387, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 1, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 5, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 5, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 1]], [[3, 5, 4, 1, 2], [1, 0, 0, 1]]} "Class ", 6388, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 5, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 5, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 1, 0, 1]]} "Class ", 6389, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 1, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 5, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 5, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 5, 4, 1, 2], [1, 1, 0, 1]]} "Class ", 6390, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 5, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 5, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 5, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 5, 3], [1, 1, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {3}, {[0, 0, 0, 0, 0, 1]}], [[1, 5, 2, 4, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 3, 4, 1], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [ [2, 5, 4, 1, 3], {2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 4, 2, 1], {4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 779, 3437, 16312, 82857, 448395, 2574518, 15624412, 99889265, 670695525, 4716713237, 34657174069, 265473027057, 2115652792090, 17509208733662] "" "Class ", 6391, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 1, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 5, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 5, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[3, 5, 4, 1, 2], [1, 0, 1, 1]]} "Class ", 6392, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 5, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 5, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 5, 4, 1, 2], [0, 1, 1, 1]]} "Class ", 6393, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 1, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 5, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 5, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 2, 1, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 5, 4, 1, 2], [1, 1, 1, 1]]} "Class ", 6394, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[3, 4, 1, 2, 5], {1, 2}, {}], [[3, 5, 1, 2, 4], {1, 2}, {}], [[4, 5, 1, 2, 3], {1, 2}, {}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 807, 3689, 18245, 96883, 549081, 3304243, 21018969, 140798765, 989933509, 7284131855, 55950197985, 447596639067, 3721737026483, 32105360571095] "" "Class ", 6395, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {[1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 765, 3309, 15307, 75364, 392997, 2160592, 12472736, 75345327, 474869974, 3114636308, 21211840660, 149698758137, 1092811596629, 8238598838230] "" "Class ", 6396, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 5, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 1, 0, 0]]} "Class ", 6397, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 5, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 0, 0]]} "Class ", 6398, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {4}, {}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 2, 4], {4}, {}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {2, 3}, {}], [[4, 5, 1, 2, 3], {4}, {}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 765, 3308, 15286, 75112, 390701, 2142863, 12350701, 74584957, 470686399, 3096788707, 21196979772, 150657864797, 1109980407513, 8463725414681] "" "Class ", 6399, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {[1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {4}, {[1, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 2, 4], {4}, {[1, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {2, 3}, {}], [[4, 5, 1, 2, 3], {3}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 732, 2969, 12452, 53769, 238379, 1082807, 5031130, 23878644, 115627763, 570641676, 2867506043, 14659426207, 76184919983, 402215173670] "" "Class ", 6400, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 5, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 5, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3, 5], [0, 1, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 0, 0, 1]}], [[4, 1, 3, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [5, 1, 4, 3, 2], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [5, 2, 4, 3, 1], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 3, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 765, 3308, 15286, 75112, 390701, 2142863, 12350701, 74584957, 470686399, 3096788707, 21196979772, 150657864797, 1109980407513, 8463725414681] "" "Class ", 6401, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 5, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 5, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3, 5], [0, 1, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 0, 0, 1]}], [[4, 1, 3, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 3, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 732, 2969, 12452, 53769, 238379, 1082807, 5031130, 23878644, 115627763, 570641676, 2867506043, 14659426207, 76184919983, 402215173670] "" "Class ", 6402, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 5, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 5, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 793, 3562, 17262, 89684, 496894, 2922141, 18165176, 118937554, 817644030, 5885082985, 44237620651, 346498959821, 2822275646421, 23860709047645] "" "Class ", 6403, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 0, 0, 1]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 748, 3130, 13775, 63545, 306455, 1541401, 8067767, 43849073, 246993312, 1439303088, 8662880822, 53775647940, 343836778725, 2261741753191] "" "Class ", 6404, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 5, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 1, 0, 1]]} "Class ", 6405, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 5, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 0, 1]]} "Class ", 6406, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 5, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 5, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3, 5], [1, 1, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 0, 0, 1]}], [[4, 1, 3, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [5, 1, 4, 3, 2], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [ [5, 2, 4, 3, 1], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 750, 3165, 14149, 66762, 331271, 1722754, 9362279, 53034827, 312456983, 1910706396, 12105437557, 79329028253, 536903957180, 3747817478325] "" "Class ", 6407, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 5, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3, 5], [1, 1, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 0, 0, 1]}], [[4, 1, 3, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 187, 716, 2812, 11222, 45280, 184202, 754182, 3104153, 12833019, 53254414, 221720224, 925768236, 3875274282, 16258705798, 68352118730] "" "Class ", 6408, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 5, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 5, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3, 5], [1, 1, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 0, 0, 1]}], [[4, 1, 3, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [5, 1, 4, 3, 2], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [ [5, 2, 4, 3, 1], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 750, 3165, 14149, 66762, 331271, 1722754, 9362279, 53034827, 312456983, 1910706396, 12105437557, 79329028253, 536903957180, 3747817478325] "" "Class ", 6409, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 5, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 2, 3, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 5, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3, 5], [1, 1, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 3, 4, 1, 2], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 0, 0, 1]}], [[4, 1, 3, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 187, 716, 2812, 11222, 45280, 184202, 754182, 3104153, 12833019, 53254414, 221720224, 925768236, 3875274282, 16258705798, 68352118730] "" "Class ", 6410, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 5, 4], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 5, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 828, 3853, 19442, 105506, 611672, 3767648, 24542311, 168396558, 1212935545, 9143920787, 71957453717, 589731775211, 5022999722058, 44380000283101] "" "Class ", 6411, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 5, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 5, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 815, 3737, 18533, 98686, 560827, 3384201, 21589851, 145070230, 1023337381, 7556462383, 58259428033, 467917879538, 3906944934521, 33850401540999] "" "Class ", 6412, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 5, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 5, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 5, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 5, 4], [0, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 763, 3275, 14945, 72210, 368121, 1973863, 11100775, 65312294, 401090351, 2565591651, 17060988933, 117743457754, 841962671965, 6229249601951] "" "Class ", 6413, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 1, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 5, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 5, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 1, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 5, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 5, 4], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {3}, {[0, 1, 0, 0, 0]}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {4}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {4}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {4}, {}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2}, {[0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {4}, {}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {4}, {}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 763, 3275, 14945, 72210, 368121, 1973863, 11100775, 65312294, 401090351, 2565591651, 17060988933, 117743457754, 841962671965, 6229249601951] "" "Class ", 6414, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {}, {}], [[2, 3, 1, 4, 5], {1, 2}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {4}, {}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 1, 5], {3}, {}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 2, 4], {4}, {}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {3}, {}], [[3, 5, 2, 4, 1], {2, 3}, {}], [[4, 5, 1, 2, 3], {4}, {}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {3}, {}], [[4, 5, 2, 3, 1], {3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 792, 3547, 17093, 87960, 480453, 2772231, 16829832, 107128922, 712872715, 4946084182, 35699075276, 267492513700, 2076975406358, 16683999428882] "" "Class ", 6415, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {3}, {[0, 1, 0, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {4}, {}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 2, 4], {4}, {}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {2, 3}, {}], [[4, 5, 1, 2, 3], {4}, {}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 778, 3415, 16020, 79769, 419378, 2318235, 13427434, 81255068, 512449881, 3360961234, 22880765733, 161417071155, 1178292328361, 8887854236741] "" "Class ", 6416, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 5, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 5, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 1, 0]]} "Class ", 6417, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 1, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 5, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 5, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 5, 3, 1, 2], [1, 1, 1, 0]]} "Class ", 6418, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 5, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 5, 4], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 5, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 5, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 828, 3853, 19442, 105506, 611672, 3767648, 24542311, 168396558, 1212935545, 9143920787, 71957453717, 589731775211, 5022999722058, 44380000283101] "" "Class ", 6419, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 1, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 5, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 5, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 1, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 5, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 5, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 815, 3737, 18533, 98686, 560827, 3384201, 21589851, 145070230, 1023337381, 7556462383, 58259428033, 467917879538, 3906944934521, 33850401540999] "" "Class ", 6420, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 5, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 5, 4], [1, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 763, 3275, 14945, 72210, 368121, 1973863, 11100775, 65312294, 401090351, 2565591651, 17060988933, 117743457754, 841962671965, 6229249601951] "" "Class ", 6421, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 1, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 5, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 5, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 1, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 5, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 5, 4], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {3}, {[0, 1, 0, 0, 0]}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {4}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {4}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {4}, {}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2}, {[0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {4}, {}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {4}, {}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 763, 3275, 14945, 72210, 368121, 1973863, 11100775, 65312294, 401090351, 2565591651, 17060988933, 117743457754, 841962671965, 6229249601951] "" "Class ", 6422, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 5, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 5, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]} "Class ", 6423, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 1, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 5, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 5, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[4, 5, 3, 1, 2], [1, 0, 1, 1]]} "Class ", 6424, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 5, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 5, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]} "Class ", 6425, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 1, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 5, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 5, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 3, 1, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 5, 3, 1, 2], [1, 1, 1, 1]]} "Class ", 6426, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 819, 3793, 19068, 103178, 596829, 3669626, 23868875, 163577578, 1177027502, 8865555004, 69715087310, 570986623065, 4860603581673, 42923906624893] "" "Class ", 6427, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 766, 3332, 15623, 78807, 426219, 2460904, 15099646, 98028860, 670718633, 4819577883, 36259971555, 284854515430, 2331084802834, 19829311155860] "" "Class ", 6428, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 5, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 5, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 0, 0, 1]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 2, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 3, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [5, 3, 4, 2, 1], {2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 4, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 766, 3329, 15557, 77928, 416832, 2371123, 14286223, 90825146, 607197578, 4255599957, 31182999369, 238313748124, 1895448901924, 15658803004391] "" "Class ", 6429, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 0, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {2}, {[0, 0, 0, 1]}], [[3, 2, 1], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 2, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 187, 715, 2795, 11051, 43947, 175275, 700075, 2798251, 11188907, 44747435, 178973355, 715860651, 2863377067, 11453377195, 45813246635] "" "Class ", 6430, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {}, {}], [[2, 3, 1, 4, 5], {1, 2}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {4}, {}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 1, 5], {3}, {}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 2, 4], {4}, {}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {3}, {}], [[3, 5, 2, 4, 1], {2, 3}, {}], [[4, 5, 1, 2, 3], {4}, {}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {3}, {}], [[4, 5, 2, 3, 1], {3}, {}], [[4, 5, 3, 1, 2], {3}, {}], [[4, 5, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 806, 3681, 18218, 96948, 551169, 3329763, 21279054, 143287018, 1013224860, 7501719166, 58000746088, 467209064974, 3912789316512, 34004906425627] "" "Class ", 6431, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {4}, {}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 2, 4], {4}, {}], [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {2, 3}, {}], [[4, 5, 1, 2, 3], {4}, {}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3, 4}, {[1, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 750, 3168, 14216, 67655, 340656, 1809572, 10110785, 59252833, 363256602, 2324160161, 15485692070, 107240146013, 770500979675, 5734194312703] "" "Class ", 6432, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 5, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 0]]} "Class ", 6433, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4, 5], [0, 1, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {2}, {[0, 0, 0, 1]}], [[3, 2, 1], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 2, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 187, 715, 2795, 11051, 43947, 175275, 700075, 2798251, 11188907, 44747435, 178973355, 715860651, 2863377067, 11453377195, 45813246635] "" "Class ", 6434, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 819, 3793, 19068, 103178, 596829, 3669626, 23868875, 163577578, 1177027502, 8865555004, 69715087310, 570986623065, 4860603581673, 42923906624893] "" "Class ", 6435, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 766, 3332, 15623, 78807, 426219, 2460904, 15099646, 98028860, 670718633, 4819577883, 36259971555, 284854515430, 2331084802834, 19829311155860] "" "Class ", 6436, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 0, 0, 1]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 3, 4, 1, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [5, 3, 4, 2, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 766, 3329, 15557, 77928, 416832, 2371123, 14286223, 90825146, 607197578, 4255599957, 31182999369, 238313748124, 1895448901924, 15658803004391] "" "Class ", 6437, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4, 5], [1, 0, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {2}, {[0, 0, 0, 1]}], [[3, 2, 1], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 187, 715, 2795, 11051, 43947, 175275, 700075, 2798251, 11188907, 44747435, 178973355, 715860651, 2863377067, 11453377195, 45813246635] "" "Class ", 6438, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 5, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]} "Class ", 6439, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 5, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {2}, {[0, 0, 0, 1]}], [[3, 2, 1], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [5, 4, 1, 3, 2], {1, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [5, 4, 2, 3, 1], {1, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 749, 3148, 13974, 65321, 320670, 1648966, 8860255, 49632648, 289239212, 1750134955, 10975808922, 71226621744, 477570355124, 3303865571895] "" "Class ", 6440, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 5, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 1]]} "Class ", 6441, " is:" {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[4, 5, 3, 2, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 5, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4, 5], [1, 1, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {2}, {[0, 0, 0, 1]}], [[3, 2, 1], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 187, 715, 2795, 11051, 43947, 175275, 700075, 2798251, 11188907, 44747435, 178973355, 715860651, 2863377067, 11453377195, 45813246635] "" "Class ", 6442, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}], [[4, 1, 2, 3, 5], {1, 3, 4}, {}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 822, 3769, 18630, 98507, 553667, 3291334, 20605711, 135360555, 930067278, 6665886353, 49712248302, 384938543360, 3088892663642, 25641408466144] "" "Class ", 6443, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 4, 5, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 2, 1, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 4, 5, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 2, 1, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {1, 3}, {[0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 809, 3649, 17660, 90967, 495780, 2845424, 17125390, 107717107, 705989475, 4809069825, 33970435644, 248345725805, 1875688786780, 14612588024530] "" "Class ", 6444, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 4, 5, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 2, 1, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 4, 3, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 3, 4, 5, 1], [0, 1, 0, 0]]} "Class ", 6445, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 4, 5, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 2, 1, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 4, 3, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 3, 4, 5, 1], [1, 1, 0, 0]]} "Class ", 6446, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 4, 5, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 4, 3, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[2, 3, 4, 5, 1], [0, 0, 1, 0]]} "Class ", 6447, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 4, 5, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 2, 1, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 4, 3, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[2, 3, 4, 5, 1], [1, 0, 1, 0]]} "Class ", 6448, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 4, 5, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 2, 1, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 4, 3, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 3, 4, 5, 1], [0, 1, 1, 0]]} "Class ", 6449, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 4, 5, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 2, 1, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 4, 3, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 3, 4, 5, 1], [1, 1, 1, 0]]} "Class ", 6450, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}], [[4, 1, 2, 3, 5], {1, 3, 4}, {}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 789, 3495, 16545, 83142, 441009, 2457963, 14339835, 87281820, 552702609, 3632275683, 24719681601, 173880087210, 1261984254525, 9435921363783] "" "Class ", 6451, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 4, 5, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 2, 1, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 4, 5, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 2, 1, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {1, 3}, {[0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 773, 3336, 15207, 72697, 362447, 1876392, 10051083, 55544661, 315899245, 1845139684, 11048651523, 67719859612, 424287619507, 2714074517843] "" "Class ", 6452, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 4, 5, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 2, 1, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 4, 3, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 3, 4, 5, 1], [0, 1, 0, 1]]} "Class ", 6453, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 4, 5, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 2, 1, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 4, 3, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 3, 4, 5, 1], [1, 1, 0, 1]]} "Class ", 6454, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 4, 5, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 4, 3, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 4, 5, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 4, 3, 2], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}], [[4, 1, 2, 3, 5], {3, 4}, {}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 789, 3495, 16545, 83142, 441009, 2457963, 14339835, 87281820, 552702609, 3632275683, 24719681601, 173880087210, 1261984254525, 9435921363783] "" "Class ", 6455, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 4, 5, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 2, 1, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 4, 5, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 2, 1, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}], [[4, 1, 2, 3], {3}, {[0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 773, 3336, 15207, 72697, 362447, 1876392, 10051083, 55544661, 315899245, 1845139684, 11048651523, 67719859612, 424287619507, 2714074517843] "" "Class ", 6456, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 4, 5, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 2, 1, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 4, 3, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 3, 4, 5, 1], [0, 1, 1, 1]]} "Class ", 6457, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 4, 5, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 3, 4, 5, 1], [1, 1, 1, 1]]} "Class ", 6458, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 2, 4, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 4, 5, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 2, 1, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 4, 2, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 2, 4, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 1, 2, 4, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 4, 5, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 2, 1, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 4, 2, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 1, 2, 4, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {1, 3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 863, 4004, 19983, 106465, 601763, 3589853, 22505449, 147731370, 1012212677, 7219461008, 53473370699, 410446055718, 3258716280600, 26716507826827] "" "Class ", 6459, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 2, 4, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 4, 5, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 2, 1, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 4, 2, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 2, 4, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 2, 4, 5, 1], [1, 1, 0, 0]]} "Class ", 6460, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 2, 4, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 4, 5, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 2, 1, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 4, 2, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 2, 4, 3], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[3, 2, 4, 5, 1], [1, 0, 1, 0]]} "Class ", 6461, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 2, 4, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 4, 5, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 2, 1, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 4, 2, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 2, 4, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 2, 4, 5, 1], [1, 1, 1, 0]]} "Class ", 6462, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 2, 4, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 4, 5, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 2, 1, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 2, 4, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 1, 2, 4, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 4, 5, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 2, 1, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 1, 2, 4, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 859, 3931, 19119, 97921, 524460, 2921730, 16858380, 100405010, 615519965, 3874925015, 25001381089, 165049371943, 1113222988121, 7661588927073] "" "Class ", 6463, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 2, 4, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 4, 5, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 2, 1, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 4, 2, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 2, 4, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 2, 4, 5, 1], [1, 1, 0, 1]]} "Class ", 6464, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 2, 4, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 4, 5, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 2, 1, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 4, 2, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 2, 4, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 1, 2, 4, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 4, 5, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 2, 1, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 4, 2, 3], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 1, 2, 4, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}], [[4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 859, 3931, 19119, 97921, 524460, 2921730, 16858380, 100405010, 615519965, 3874925015, 25001381089, 165049371943, 1113222988121, 7661588927073] "" "Class ", 6465, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 2, 4, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 4, 5, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 2, 1, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 4, 2, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 2, 4, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 2, 4, 5, 1], [1, 1, 1, 1]]} "Class ", 6466, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 3, 2, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 3, 5, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 3, 1, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 3, 4, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 3, 2, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 4, 3, 5, 1], [0, 1, 0, 0]]} "Class ", 6467, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 3, 2, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 3, 5, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 3, 1, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 3, 4, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 3, 2, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 4, 3, 5, 1], [1, 1, 0, 0]]} "Class ", 6468, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 3, 2, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 3, 5, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 3, 1, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 3, 4, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 3, 2, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 4, 3, 5, 1], [0, 1, 1, 0]]} "Class ", 6469, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 3, 2, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 3, 5, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 3, 1, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 3, 4, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 3, 2, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 4, 3, 5, 1], [1, 1, 1, 0]]} "Class ", 6470, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 3, 2, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 3, 5, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 3, 1, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 3, 4, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 3, 2, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 4, 3, 5, 1], [0, 1, 0, 1]]} "Class ", 6471, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 3, 2, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 3, 5, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 3, 1, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 3, 4, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 3, 2, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 4, 3, 5, 1], [1, 1, 0, 1]]} "Class ", 6472, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 3, 2, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 3, 5, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 3, 1, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 3, 4, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 3, 2, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 4, 3, 5, 1], [0, 1, 1, 1]]} "Class ", 6473, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 3, 2, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 3, 5, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 3, 1, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 3, 4, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 3, 2, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 4, 3, 5, 1], [1, 1, 1, 1]]} "Class ", 6474, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 3, 4, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 3, 5, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 3, 1, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 3, 2, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 3, 4, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 1, 3, 4, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 3, 5, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 3, 1, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 3, 2, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 1, 3, 4, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 863, 4004, 19983, 106465, 601763, 3589853, 22505449, 147731370, 1012212677, 7219461008, 53473370699, 410446055718, 3258716280600, 26716507826827] "" "Class ", 6475, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 3, 4, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 3, 5, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 3, 1, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 3, 2, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 3, 4, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 2, 3, 5, 1], [1, 1, 0, 0]]} "Class ", 6476, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 3, 4, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 3, 5, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 3, 1, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 3, 2, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 3, 4, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[4, 2, 3, 5, 1], [1, 0, 1, 0]]} "Class ", 6477, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 3, 4, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 3, 5, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 3, 1, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 3, 2, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 3, 4, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 2, 3, 5, 1], [1, 1, 1, 0]]} "Class ", 6478, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 3, 4, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 3, 5, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 3, 1, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 3, 2, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 3, 4, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 1, 3, 4, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 3, 5, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 3, 1, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 3, 2, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 1, 3, 4, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {2}, {[0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 859, 3931, 19119, 97921, 524460, 2921730, 16858380, 100405010, 615519965, 3874925015, 25001381089, 165049371943, 1113222988121, 7661588927073] "" "Class ", 6479, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 3, 4, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 3, 5, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 3, 1, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 3, 2, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 3, 4, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 2, 3, 5, 1], [1, 1, 0, 1]]} "Class ", 6480, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 3, 4, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 3, 5, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 3, 1, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 3, 2, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 3, 4, 2], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 1, 3, 4, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 3, 5, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 3, 1, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 3, 2, 4], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 1, 3, 4, 2], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}], [[4, 1, 2, 3], {2}, {[0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 859, 3931, 19119, 97921, 524460, 2921730, 16858380, 100405010, 615519965, 3874925015, 25001381089, 165049371943, 1113222988121, 7661588927073] "" "Class ", 6481, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 3, 4, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 3, 5, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 3, 1, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 3, 2, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 3, 4, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 2, 3, 5, 1], [1, 1, 1, 1]]} "Class ", 6482, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 4, 2, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 2, 5, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 4, 1, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 2, 4, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 4, 2, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 4, 2, 5, 1], [0, 1, 0, 0]]} "Class ", 6483, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 4, 2, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 2, 5, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 4, 1, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 2, 4, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 4, 2, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 4, 2, 5, 1], [1, 1, 0, 0]]} "Class ", 6484, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 4, 2, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 2, 5, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 4, 1, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 2, 4, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 4, 2, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 4, 2, 5, 1], [0, 1, 1, 0]]} "Class ", 6485, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 4, 2, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 2, 5, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 4, 1, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 2, 4, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 4, 2, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 4, 2, 5, 1], [1, 1, 1, 0]]} "Class ", 6486, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 4, 2, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 2, 5, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 4, 1, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 2, 4, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 4, 2, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 4, 2, 5, 1], [0, 1, 0, 1]]} "Class ", 6487, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 4, 2, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 2, 5, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 4, 1, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 2, 4, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 4, 2, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 4, 2, 5, 1], [1, 1, 0, 1]]} "Class ", 6488, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 4, 2, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 2, 5, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 4, 1, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 2, 4, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 4, 2, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 4, 2, 5, 1], [0, 1, 1, 1]]} "Class ", 6489, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 4, 2, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 2, 5, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 4, 1, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 2, 4, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 4, 2, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 4, 2, 5, 1], [1, 1, 1, 1]]} "Class ", 6490, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 4, 3, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 3, 2, 5, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 4, 1, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 2, 3, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 4, 3, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 3, 2, 5, 1], [1, 1, 0, 0]]} "Class ", 6491, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 4, 3, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 3, 2, 5, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 4, 1, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 2, 3, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 4, 3, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 3, 2, 5, 1], [1, 1, 1, 0]]} "Class ", 6492, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 4, 3, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 3, 2, 5, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 4, 1, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 2, 3, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 4, 3, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 3, 2, 5, 1], [1, 1, 0, 1]]} "Class ", 6493, " is:" {{[[1, 3, 2], [1, 0]], [[5, 1, 4, 3, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 3, 2, 5, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 4, 1, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 5, 2, 3, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 1, 4, 3, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 3, 2, 5, 1], [1, 1, 1, 1]]} "Class ", 6494, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 4, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 2, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 5, 3, 2], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 4, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 2, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 5, 3, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}], [[4, 2, 1, 3, 5], {1, 2, 4}, {}], [[5, 2, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 834, 3876, 19496, 105304, 606898, 3712810, 24004328, 163389715, 1167018770, 8721595318, 68025368984, 552479196761, 4662795834336, 40819208828899] "" "Class ", 6495, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 4, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 2, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 5, 3, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 4, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 2, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 5, 3, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 822, 3774, 18725, 99647, 565467, 3405242, 21670141, 145204315, 1021239339, 7517789410, 57780949627, 462636521741, 3851054079078, 33266660624490] "" "Class ", 6496, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 4, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 2, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 5, 3, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 3, 5, 4, 1], [0, 1, 0, 0]]} "Class ", 6497, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 4, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 2, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 5, 3, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 3, 5, 4, 1], [1, 1, 0, 0]]} "Class ", 6498, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 4, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 2, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 5, 3, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[2, 3, 5, 4, 1], [0, 0, 1, 0]]} "Class ", 6499, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 4, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 2, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 5, 3, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[2, 3, 5, 4, 1], [1, 0, 1, 0]]} "Class ", 6500, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 4, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 2, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 5, 3, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 3, 5, 4, 1], [0, 1, 1, 0]]} "Class ", 6501, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 4, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 2, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 5, 3, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 3, 5, 4, 1], [1, 1, 1, 0]]} "Class ", 6502, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 4, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 2, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 5, 3, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 4, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 2, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 5, 3, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {}], [[4, 2, 1, 3, 5], {1, 2, 4}, {}], [[5, 2, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 803, 3634, 17742, 92838, 517793, 3063645, 19151463, 126038855, 870539098, 6292882515, 47491348067, 373352511267, 3051361600267, 25879134937192] "" "Class ", 6503, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 4, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 2, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 4, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 2, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 789, 3502, 16668, 84610, 456060, 2600755, 15641946, 98943068, 656580640, 4560329373, 33081415173, 250145673041, 1967997933873, 16081849997300] "" "Class ", 6504, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 4, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 2, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 5, 3, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 3, 5, 4, 1], [0, 1, 0, 1]]} "Class ", 6505, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 4, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 2, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 5, 3, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 3, 5, 4, 1], [1, 1, 0, 1]]} "Class ", 6506, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 4, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 2, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 5, 3, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[2, 3, 5, 4, 1], [0, 0, 1, 1]]} "Class ", 6507, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 4, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 2, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 5, 3, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[2, 3, 5, 4, 1], [1, 0, 1, 1]]} "Class ", 6508, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 4, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 2, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 5, 3, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 3, 5, 4, 1], [0, 1, 1, 1]]} "Class ", 6509, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 5, 4, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 3, 1, 2, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 5, 3, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 1, 3, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 3, 5, 4, 1], [1, 1, 1, 1]]} "Class ", 6510, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 1, 4, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 5, 4, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 1, 2, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 5, 2, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 1, 4, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 2, 1, 4, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 5, 4, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 1, 2, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 5, 2, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 2, 1, 4, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {[0, 0, 1, 0, 0]}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 864, 4023, 20215, 108843, 624286, 3795794, 24364981, 164526009, 1165108894, 8629385463, 66684343906, 536484967793, 4484692434644, 38884833327662] "" "Class ", 6511, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 1, 4, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 5, 4, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 1, 2, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 5, 2, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 1, 4, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 2, 5, 4, 1], [1, 1, 0, 0]]} "Class ", 6512, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 1, 4, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 5, 4, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 1, 2, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 5, 2, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 1, 4, 3], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[3, 2, 5, 4, 1], [1, 0, 1, 0]]} "Class ", 6513, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 1, 4, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 5, 4, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 1, 2, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 5, 2, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 1, 4, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 2, 5, 4, 1], [1, 1, 1, 0]]} "Class ", 6514, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 1, 4, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 5, 4, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 1, 2, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 5, 2, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 1, 4, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 2, 1, 4, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 5, 4, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 1, 2, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 5, 2, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 2, 1, 4, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 861, 3972, 19649, 103536, 578163, 3407676, 21128333, 137416665, 935209502, 6645421883, 49206598694, 378992185756, 3031275961641, 25138840826540] "" "Class ", 6515, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 1, 4, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 5, 4, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 1, 2, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 5, 2, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 1, 4, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 2, 5, 4, 1], [1, 1, 0, 1]]} "Class ", 6516, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 1, 4, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 5, 4, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 1, 2, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 5, 2, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 1, 4, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[3, 2, 5, 4, 1], [1, 0, 1, 1]]} "Class ", 6517, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 1, 4, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 5, 4, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 4, 1, 2, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 5, 2, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 1, 4, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 2, 5, 4, 1], [1, 1, 1, 1]]} "Class ", 6518, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 3, 4, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 3, 2, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 5, 2], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 3, 4, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 3, 2, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 5, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {1, 3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {}], [[4, 2, 3, 1, 5], {1, 2, 3}, {}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2}, {}], [[5, 3, 4, 1, 2], {1, 2}, {}], [[5, 3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 834, 3876, 19496, 105304, 606898, 3712810, 24004328, 163389715, 1167018770, 8721595318, 68025368984, 552479196761, 4662795834336, 40819208828899] "" "Class ", 6519, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 3, 4, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 3, 2, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 5, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 3, 4, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 3, 2, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 5, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {1, 3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 802, 3619, 17584, 91426, 506059, 2968711, 18386882, 119835229, 819453385, 5863918677, 43807864290, 340950961407, 2759093794444, 23174344383405] "" "Class ", 6520, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 3, 4, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 3, 2, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 5, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 5, 3, 4, 1], [0, 1, 0, 0]]} "Class ", 6521, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 3, 4, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 3, 2, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 5, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 3, 4, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 3, 2, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 5, 2], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 1, 2, 4, 5], {4}, {}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 3, 5], {4}, {}], [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 3, 5, 1], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}], [[5, 1, 2, 3, 4], {4}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 761, 3241, 14571, 68790, 339616, 1747411, 9343064, 51783580, 296874467, 1757224254, 10721530568, 67336615665, 434782637842, 2882965835059] "" "Class ", 6522, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 3, 4, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 3, 2, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 5, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[2, 5, 3, 4, 1], [0, 0, 1, 0]]} "Class ", 6523, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 3, 4, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 3, 2, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 5, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[2, 5, 3, 4, 1], [1, 0, 1, 0]]} "Class ", 6524, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 3, 4, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 3, 2, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 5, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 5, 3, 4, 1], [0, 1, 1, 0]]} "Class ", 6525, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 3, 4, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 3, 2, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 5, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 5, 3, 4, 1], [1, 1, 1, 0]]} "Class ", 6526, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 3, 4, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 3, 2, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 5, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 3, 4, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 3, 2, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 5, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {}], [[4, 2, 3, 1, 5], {1, 2, 3}, {}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {2, 3}, {}], [[5, 3, 4, 1, 2], {2, 3}, {}], [[5, 3, 4, 2, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 804, 3646, 17845, 93644, 523900, 3109648, 19501471, 128752376, 892078074, 6468403288, 48961942463, 386029724594, 3163823869930, 26905707777479] "" "Class ", 6527, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 3, 4, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 3, 2, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 5, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 3, 4, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 3, 2, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 5, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 763, 3270, 14844, 70961, 355673, 1862785, 10165879, 57673186, 339443431, 2068967527, 13039101751, 84846212977, 569306441734, 3934345877165] "" "Class ", 6528, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 3, 4, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 3, 2, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 5, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 5, 3, 4, 1], [0, 1, 0, 1]]} "Class ", 6529, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 3, 4, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 3, 2, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 5, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 5, 3, 4, 1], [1, 1, 0, 1]]} "Class ", 6530, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 3, 4, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 3, 2, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 5, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 3, 4, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 3, 2, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 5, 2], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {}], [[4, 2, 3, 1, 5], {2, 3}, {}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {2, 3}, {}], [[5, 3, 4, 1, 2], {2, 3}, {}], [[5, 3, 4, 2, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 804, 3646, 17845, 93644, 523900, 3109648, 19501471, 128752376, 892078074, 6468403288, 48961942463, 386029724594, 3163823869930, 26905707777479] "" "Class ", 6531, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 3, 4, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 3, 2, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 5, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 3, 4, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 3, 2, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 5, 2], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 763, 3270, 14844, 70961, 355673, 1862785, 10165879, 57673186, 339443431, 2068967527, 13039101751, 84846212977, 569306441734, 3934345877165] "" "Class ", 6532, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 3, 4, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 3, 2, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 5, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 5, 3, 4, 1], [0, 1, 1, 1]]} "Class ", 6533, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 3, 4, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 3, 2, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 5, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 3, 1, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 5, 3, 4, 1], [1, 1, 1, 1]]} "Class ", 6534, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 3, 4, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 3, 2, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 2, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 3, 4, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 3, 2, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 2, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}], [[4, 1, 2, 3, 5], {1, 3, 4}, {}], [[5, 1, 2, 3, 4], {1, 3, 4}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 805, 3666, 18043, 95191, 535096, 3189665, 20078173, 132973113, 923570613, 6708664018, 50839097250, 401053670460, 3286934498076, 27937500829673] "" "Class ", 6535, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 3, 4, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 2, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 3, 4, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 2, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {1, 3}, {[1, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 778, 3420, 16116, 80894, 430048, 2409448, 14168111, 87132464, 558764865, 3726863697, 25795630409, 184914584967, 1370391521080, 10482633844085] "" "Class ", 6536, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 3, 4, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 3, 2, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 2, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 2, 3, 4, 1], [0, 1, 0, 0]]} "Class ", 6537, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 3, 4, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 2, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 2, 3, 4, 1], [1, 1, 0, 0]]} "Class ", 6538, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 3, 4, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 3, 2, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 2, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[5, 2, 3, 4, 1], [0, 0, 1, 0]]} "Class ", 6539, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 3, 4, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 2, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[5, 2, 3, 4, 1], [1, 0, 1, 0]]} "Class ", 6540, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 3, 4, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 3, 2, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 2, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 2, 3, 4, 1], [0, 1, 1, 0]]} "Class ", 6541, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 3, 4, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 2, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 2, 3, 4, 1], [1, 1, 1, 0]]} "Class ", 6542, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 3, 4, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 3, 2, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 2, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 3, 4, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 3, 2, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 2, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}], [[4, 1, 2, 3, 5], {1, 3, 4}, {}], [[5, 1, 2, 3, 4], {3}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 762, 3257, 14734, 70164, 350173, 1824916, 9900831, 55776020, 325541041, 1964740513, 12240641505, 78603636042, 519551554402, 3530432003317] "" "Class ", 6543, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 3, 4, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 3, 4, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {}, {[1, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}], [[4, 1, 2, 3, 5], {1, 3, 4}, {[1, 0, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {2}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 747, 3111, 13551, 61419, 288543, 1400727, 7008519, 36065919, 190531623, 1031674935, 5717624727, 32392623783, 187392817623, 1105868383095] "" "Class ", 6544, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 3, 4, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 3, 2, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 2, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 2, 3, 4, 1], [0, 1, 0, 1]]} "Class ", 6545, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 3, 4, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 2, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 2, 3, 4, 1], [1, 1, 0, 1]]} "Class ", 6546, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 3, 4, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 3, 2, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 2, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 3, 4, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 3, 2, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 2, 5], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}], [[4, 1, 2, 3, 5], {3, 4}, {}], [[5, 1, 2, 3, 4], {3}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 762, 3257, 14734, 70164, 350173, 1824916, 9900831, 55776020, 325541041, 1964740513, 12240641505, 78603636042, 519551554402, 3530432003317] "" "Class ", 6547, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 3, 4, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 2, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[5, 2, 3, 4, 1], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 3, 4, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 3, 2, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 2, 5], [1, 1, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 2, 3, 4, 1], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 747, 3111, 13551, 61419, 288543, 1400727, 7008519, 36065919, 190531623, 1031674935, 5717624727, 32392623783, 187392817623, 1105868383095] "" "Class ", 6548, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 3, 4, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 3, 2, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 2, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 2, 3, 4, 1], [0, 1, 1, 1]]} "Class ", 6549, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 3, 4, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 3, 2, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 3, 2, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 3, 4, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 2, 3, 4, 1], [1, 1, 1, 1]]} "Class ", 6550, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 2, 4, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 4, 2, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 2, 5, 3], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 2, 4, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 4, 2, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 2, 5, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {1, 3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {}], [[4, 2, 3, 1, 5], {1, 2, 3}, {}], [[5, 2, 3, 1, 4], {1, 2, 3}, {}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {1, 2}, {}], [[5, 3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 827, 3830, 19170, 102969, 589940, 3586167, 23028688, 155636826, 1103451403, 8183761207, 63331241773, 510241188887, 4271226039578, 37081829058855] "" "Class ", 6551, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 2, 4, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 4, 2, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 2, 5, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 2, 4, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 4, 2, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 2, 5, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {1, 3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 804, 3641, 17757, 92678, 514942, 3031668, 18838333, 123139820, 844259094, 6055300766, 45327541094, 353379313419, 2863801705931, 24082999593273] "" "Class ", 6552, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 2, 4, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 4, 2, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 2, 5, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 5, 2, 4, 1], [0, 1, 0, 0]]} "Class ", 6553, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 2, 4, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 4, 2, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 2, 5, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 2, 4, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 4, 2, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 2, 5, 3], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 1, 0, 0]}], [[3, 1, 2, 4, 5], {4}, {}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 3, 5], {4}, {}], [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 3, 5, 1], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}], [[5, 1, 2, 3, 4], {4}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 777, 3401, 15889, 78693, 410897, 2252010, 12908554, 77148545, 479484267, 3091830200, 20642874392, 142448382345, 1014335180040, 7442456143905] "" "Class ", 6554, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 2, 4, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 4, 2, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 2, 5, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[3, 5, 2, 4, 1], [0, 0, 1, 0]]} "Class ", 6555, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 2, 4, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 4, 2, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 2, 5, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[3, 5, 2, 4, 1], [1, 0, 1, 0]]} "Class ", 6556, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 2, 4, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 4, 2, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 2, 5, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 5, 2, 4, 1], [0, 1, 1, 0]]} "Class ", 6557, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 2, 4, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 4, 2, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 2, 5, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 5, 2, 4, 1], [1, 1, 1, 0]]} "Class ", 6558, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 2, 4, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 4, 2, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 2, 5, 3], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 2, 4, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 4, 2, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 2, 5, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {}], [[4, 1, 2, 3, 5], {1, 3, 4}, {}], [[4, 2, 3, 1, 5], {1, 2, 3}, {}], [[5, 1, 2, 3, 4], {3}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {2, 3}, {}], [[5, 2, 3, 4, 1], {2}, {}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {2, 3}, {}], [[5, 3, 4, 2, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 792, 3546, 17088, 88048, 482583, 2801188, 17153582, 110444555, 745471832, 5261195678, 38733856020, 296849847806, 2363725317358, 19521868215367] "" "Class ", 6559, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 2, 4, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 4, 2, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 2, 5, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 2, 4, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 4, 2, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 2, 5, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0]}], [[4, 1, 2, 3, 5], {1, 3, 4}, {}], [[5, 1, 2, 3, 4], {3}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {2, 3, 4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 763, 3270, 14844, 70961, 355673, 1862785, 10165879, 57673186, 339443431, 2068967527, 13039101751, 84846212977, 569306441734, 3934345877165] "" "Class ", 6560, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 2, 4, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 4, 2, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 2, 5, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 5, 2, 4, 1], [0, 1, 0, 1]]} "Class ", 6561, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 2, 4, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 4, 2, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 2, 5, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 5, 2, 4, 1], [1, 1, 0, 1]]} "Class ", 6562, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 2, 4, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 4, 2, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 2, 5, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 2, 4, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 4, 2, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 2, 5, 3], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {}], [[4, 2, 3, 1, 5], {2, 3}, {}], [[5, 2, 3, 1, 4], {2, 3}, {}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {2, 3}, {}], [[5, 3, 4, 2, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 777, 3400, 15875, 78574, 410109, 2247666, 12889497, 77106636, 479901435, 3100362584, 20748541063, 143578840284, 1025690755493, 7553184983930] "" "Class ", 6563, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 2, 4, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 4, 2, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 2, 5, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 2, 4, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 4, 2, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 2, 5, 3], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 747, 3110, 13532, 61202, 286606, 1385818, 6904771, 35397468, 186508447, 1009179949, 5604102933, 31922266494, 186446899551, 1116196669984] "" "Class ", 6564, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 2, 4, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 4, 2, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 2, 5, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 5, 2, 4, 1], [0, 1, 1, 1]]} "Class ", 6565, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 2, 4, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 4, 2, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 2, 5, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 4, 1, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 5, 2, 4, 1], [1, 1, 1, 1]]} "Class ", 6566, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 4, 3, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 2, 4, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 4, 2, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 2, 3, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 4, 3, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 3, 2, 4, 1], [0, 1, 0, 0]]} "Class ", 6567, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 4, 3, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 2, 4, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 2, 3, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 4, 3, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 3, 2, 4, 1], [1, 1, 0, 0]]} "Class ", 6568, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 4, 3, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 2, 4, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 4, 2, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 2, 3, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 4, 3, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 3, 2, 4, 1], [0, 1, 1, 0]]} "Class ", 6569, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 4, 3, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 2, 4, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 2, 3, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 4, 3, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 3, 2, 4, 1], [1, 1, 1, 0]]} "Class ", 6570, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 4, 3, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 2, 4, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 4, 2, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 2, 3, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 4, 3, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 3, 2, 4, 1], [0, 1, 0, 1]]} "Class ", 6571, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 4, 3, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 2, 4, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 2, 3, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 4, 3, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 3, 2, 4, 1], [1, 1, 0, 1]]} "Class ", 6572, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 4, 3, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 2, 4, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 4, 2, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 2, 3, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 4, 3, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 3, 2, 4, 1], [0, 1, 1, 1]]} "Class ", 6573, " is:" {{[[1, 3, 2], [1, 0]], [[5, 2, 4, 3, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 2, 4, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 4, 2, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 4, 2, 3, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 2, 4, 3, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 3, 2, 4, 1], [1, 1, 1, 1]]} "Class ", 6574, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 5, 4, 2], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 5, 4, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {1}, {}], [[4, 3, 1, 2, 5], {1, 2, 4}, {}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 4}, {}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 197, 844, 3954, 20064, 109399, 636784, 3935724, 25712577, 176877209, 1276870353, 9644885457, 76032549428, 624102395831, 5323195552712, 47091735986454] "" "Class ", 6575, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 5, 4, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 5, 4, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 825, 3814, 19099, 102834, 591616, 3617638, 23405888, 159600585, 1143045601, 8572399149, 67141570207, 547896411330, 4648350153202, 40922351380119] "" "Class ", 6576, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 3, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 3, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 5, 4, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 4, 5, 3, 1], [0, 1, 0, 0]]} "Class ", 6577, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 3, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 3, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 5, 4, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 4, 5, 3, 1], [1, 1, 0, 0]]} "Class ", 6578, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 3, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 3, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 5, 4, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[2, 4, 5, 3, 1], [0, 0, 1, 0]]} "Class ", 6579, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 3, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 3, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 5, 4, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[2, 4, 5, 3, 1], [1, 0, 1, 0]]} "Class ", 6580, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 3, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 3, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 5, 4, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 4, 5, 3, 1], [0, 1, 1, 0]]} "Class ", 6581, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 3, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 3, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 5, 4, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 4, 5, 3, 1], [1, 1, 1, 0]]} "Class ", 6582, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 5, 4, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 5, 4, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {2}, {}], [[4, 3, 1, 2, 5], {1, 2, 4}, {}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {2, 4}, {}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 813, 3713, 18309, 96785, 545246, 3257355, 20548635, 136383553, 949347563, 6911344892, 52492915573, 415031833838, 3409134221140, 29040985312403] "" "Class ", 6583, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 5, 4, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 5, 4, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {1}, {[0, 0, 0, 1, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 789, 3500, 16616, 83857, 447466, 2513177, 14799522, 91071981, 583951826, 3891570727, 26894248605, 192362538985, 1421479845253, 10835066678862] "" "Class ", 6584, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 3, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 3, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 5, 4, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 4, 5, 3, 1], [0, 1, 0, 1]]} "Class ", 6585, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 3, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 3, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 5, 4, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 4, 5, 3, 1], [1, 1, 0, 1]]} "Class ", 6586, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 3, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 3, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 5, 4, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[2, 4, 5, 3, 1], [0, 0, 1, 1]]} "Class ", 6587, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 3, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 3, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 5, 4, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[2, 4, 5, 3, 1], [1, 0, 1, 1]]} "Class ", 6588, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 3, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 3, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 5, 4, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 4, 5, 3, 1], [0, 1, 1, 1]]} "Class ", 6589, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 4, 5, 3, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 2, 1, 3, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 5, 4, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 1, 2, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 4, 5, 3, 1], [1, 1, 1, 1]]} "Class ", 6590, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 1, 4, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 5, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 1, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 5, 2, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 1, 4, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 3, 1, 4, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 5, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 1, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 5, 2, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 3, 1, 4, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 865, 4039, 20384, 110376, 637367, 3905051, 25276185, 172198649, 1230766484, 9202674622, 71804373639, 583324505164, 4923975984840, 43109902048082] "" "Class ", 6591, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 1, 4, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 5, 3, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 1, 3, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 5, 2, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 1, 4, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 2, 5, 3, 1], [1, 1, 0, 0]]} "Class ", 6592, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 1, 4, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 5, 3, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 1, 3, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 5, 2, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 1, 4, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[4, 2, 5, 3, 1], [1, 0, 1, 0]]} "Class ", 6593, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 1, 4, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 5, 3, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 1, 3, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 5, 2, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 1, 4, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 2, 5, 3, 1], [1, 1, 1, 0]]} "Class ", 6594, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 1, 4, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 5, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 1, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 5, 2, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 1, 4, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 3, 1, 4, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 5, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 1, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 5, 2, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 3, 1, 4, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {[0, 1, 0, 0, 0]}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 862, 3989, 19834, 105220, 592302, 3522293, 22047356, 144807610, 995336625, 7142909314, 53407529333, 415277838945, 3352321893474, 28050987459898] "" "Class ", 6595, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 1, 4, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 5, 3, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 1, 3, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 5, 2, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 1, 4, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 2, 5, 3, 1], [1, 1, 0, 1]]} "Class ", 6596, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 1, 4, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 5, 3, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 1, 3, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 5, 2, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 1, 4, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[4, 2, 5, 3, 1], [1, 0, 1, 1]]} "Class ", 6597, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 1, 4, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 2, 5, 3, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 4, 1, 3, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 5, 2, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 1, 4, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 2, 5, 3, 1], [1, 1, 1, 1]]} "Class ", 6598, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {}, {}], [[4, 3, 2, 1, 5], {1, 2, 3}, {}], [[5, 3, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {1, 2, 3}, {}], [[5, 4, 3, 1, 2], {1, 2, 3}, {}], [[5, 4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 197, 844, 3954, 20064, 109399, 636784, 3935724, 25712577, 176877209, 1276870353, 9644885457, 76032549428, 624102395831, 5323195552712, 47091735986454] "" "Class ", 6599, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 817, 3764, 18796, 100996, 580250, 3545089, 22925456, 156294181, 1119386028, 8396419185, 65782033936, 536998505828, 4557813978908, 40143757372099] "" "Class ", 6600, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 3, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 3, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 5, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 5, 4, 3, 1], [0, 1, 0, 0]]} "Class ", 6601, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 3, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 3, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 5, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 3, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 3, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 5, 2], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {}, {}], [[4, 2, 1, 3], {}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 1, 0]}], [[3, 2, 1, 4, 5], {4}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 3, 5], {4}, {}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 2, 5], {4}, {}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}], [[5, 2, 1, 3, 4], {4}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {4}, {}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 4, 1, 2, 3], {4}, {}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 766, 3325, 15488, 77205, 410771, 2326226, 13980085, 88885428, 596032441, 4202664784, 31071475928, 240233331281, 1937678158634, 16268207537932] "" "Class ", 6602, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 3, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 3, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 5, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[2, 5, 4, 3, 1], [0, 0, 1, 0]]} "Class ", 6603, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 3, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 3, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 5, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[2, 5, 4, 3, 1], [1, 0, 1, 0]]} "Class ", 6604, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 3, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 3, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 5, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 5, 4, 3, 1], [0, 1, 1, 0]]} "Class ", 6605, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 3, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 3, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 5, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 5, 4, 3, 1], [1, 1, 1, 0]]} "Class ", 6606, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {}, {}], [[4, 3, 2, 1, 5], {1, 2, 3}, {}], [[5, 3, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {2, 3}, {}], [[5, 4, 3, 1, 2], {2, 3}, {}], [[5, 4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 826, 3828, 19222, 103777, 598525, 3667684, 23770685, 162303611, 1163520913, 8731455446, 68410765717, 558307228179, 4736148033115, 41683413669267] "" "Class ", 6607, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 803, 3636, 17779, 93294, 522564, 3109748, 19579807, 129953824, 906236525, 6620524677, 50536065259, 402110249253, 3328143235321, 28598241845327] "" "Class ", 6608, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 3, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 3, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 5, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 5, 4, 3, 1], [0, 1, 0, 1]]} "Class ", 6609, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 3, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 3, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 5, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 3, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 3, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 5, 2], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[3, 2, 1, 4], {}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 1, 0]}], [[3, 2, 1, 4, 5], {4}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 3, 5], {4}, {}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 2, 5], {4}, {}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}], [[5, 2, 1, 3, 4], {4}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {4}, {}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 4, 1, 2, 3], {4}, {}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 3}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 749, 3145, 13915, 64626, 314200, 1595920, 8455356, 46661372, 267855591, 1597252545, 9880530031, 63316773521, 419747266919, 2874717861744] "" "Class ", 6610, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 3, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 3, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 5, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[2, 5, 4, 3, 1], [0, 0, 1, 1]]} "Class ", 6611, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 3, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 3, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 5, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[2, 5, 4, 3, 1], [1, 0, 1, 1]]} "Class ", 6612, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 3, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 3, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 5, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[2, 5, 4, 3, 1], [0, 1, 1, 1]]} "Class ", 6613, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 5, 4, 3, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[4, 1, 2, 3, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 5, 2], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 2, 1, 4], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[2, 5, 4, 3, 1], [1, 1, 1, 1]]} "Class ", 6614, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 2, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 2, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}], [[4, 2, 1, 3, 5], {1, 2, 4}, {}], [[5, 2, 1, 3, 4], {1, 2, 4}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 819, 3795, 19082, 103195, 596239, 3660638, 23771446, 162624248, 1168029698, 8781381505, 68923728645, 563450757197, 4787583107957, 42202002946218] "" "Class ", 6615, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 2, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 2, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {[1, 0, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 794, 3585, 17549, 92463, 520953, 3121270, 19794010, 132334553, 929504212, 6838445033, 52557466995, 420972710346, 3506672574597, 30320001716084] "" "Class ", 6616, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 3, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 3, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 2, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 2, 4, 3, 1], [0, 1, 0, 0]]} "Class ", 6617, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 3, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 2, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 2, 4, 3, 1], [1, 1, 0, 0]]} "Class ", 6618, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 3, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 3, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 2, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[5, 2, 4, 3, 1], [0, 0, 1, 0]]} "Class ", 6619, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 3, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 3, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 2, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[5, 2, 4, 3, 1], [1, 0, 1, 0]]} "Class ", 6620, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 3, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 3, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 2, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 2, 4, 3, 1], [0, 1, 1, 0]]} "Class ", 6621, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 3, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 2, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 2, 4, 3, 1], [1, 1, 1, 0]]} "Class ", 6622, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 2, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 2, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {}], [[4, 2, 1, 3, 5], {1, 2, 4}, {}], [[5, 2, 1, 3, 4], {2, 4}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 794, 3584, 17528, 92197, 518260, 3096839, 19583162, 130544522, 914271071, 6707124752, 51403830000, 410609894946, 3411305910318, 29419930586323] "" "Class ", 6623, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 2, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 2, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2}, {[1, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 765, 3311, 15357, 76114, 401878, 2253057, 13367854, 83670715, 550809283, 3803092051, 27470891559, 207108522852, 1626261921157, 13274216784775] "" "Class ", 6624, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 3, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 3, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 2, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 2, 4, 3, 1], [0, 1, 0, 1]]} "Class ", 6625, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 3, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 2, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 2, 4, 3, 1], [1, 1, 0, 1]]} "Class ", 6626, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 3, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 3, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 2, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[5, 2, 4, 3, 1], [0, 0, 1, 1]]} "Class ", 6627, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 3, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 3, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 2, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[5, 2, 4, 3, 1], [1, 0, 1, 1]]} "Class ", 6628, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 3, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 3, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 2, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 2, 4, 3, 1], [0, 1, 1, 1]]} "Class ", 6629, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 2, 4, 3, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 4, 2, 3, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 4, 2, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 2, 4, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 2, 4, 3, 1], [1, 1, 1, 1]]} "Class ", 6630, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 5, 4], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 5, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {1, 3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {}], [[4, 2, 3, 1, 5], {1, 2, 3}, {}], [[5, 2, 3, 1, 4], {1, 2, 3}, {}], [[5, 2, 4, 1, 3], {1, 2}, {}], [[5, 3, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 829, 3861, 19480, 105634, 611778, 3763610, 24481465, 167723530, 1206168915, 9078128427, 71322348661, 583565048037, 4962339790689, 43773011811208] "" "Class ", 6631, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 2, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 5, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 2, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 5, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {1, 3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 816, 3747, 18600, 99091, 563183, 3397234, 21655294, 145326006, 1023415836, 7541341092, 58000629476, 464540879263, 3866715517334, 33388198499491] "" "Class ", 6632, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 5, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 5, 4], [0, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 0, 1]}], [[4, 5, 1, 3, 2], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 777, 3403, 15936, 79350, 418167, 2323196, 13560993, 82925473, 529840266, 3529025488, 24451917114, 175914880946, 1311844675476, 10124562485120] "" "Class ", 6633, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 5, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 5, 4], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 1, 0, 0, 0]}], [[3, 1, 2, 4, 5], {4}, {}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 3, 1, 5], {4}, {[0, 1, 0, 0, 0, 0]}], [[4, 2, 3, 5, 1], {4}, {[0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {2, 3}, {[0, 1, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 777, 3403, 15936, 79350, 418167, 2323196, 13560993, 82925473, 529840266, 3529025488, 24451917114, 175914880946, 1311844675476, 10124562485120] "" "Class ", 6634, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 5, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [0, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 0, 1, 0]]} "Class ", 6635, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 2, 3, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 5, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [0, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[4, 5, 2, 3, 1], [1, 0, 1, 0]]} "Class ", 6636, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 5, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 1, 0]]} "Class ", 6637, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 5, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 1, 0]]} "Class ", 6638, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 5, 4], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 5, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {}], [[4, 1, 2, 3, 5], {1, 3, 4}, {}], [[4, 2, 3, 1, 5], {1, 2, 3}, {}], [[5, 1, 2, 3, 4], {3}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {2, 3}, {}], [[5, 2, 3, 4, 1], {2}, {}], [[5, 2, 4, 1, 3], {2, 3}, {}], [[5, 3, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 790, 3517, 16798, 85473, 460667, 2617411, 15615514, 97491178, 635068945, 4305299826, 30305695631, 221057067281, 1667851230301, 12994962875102] "" "Class ", 6639, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 2, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 5, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 2, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 5, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3, 5], {1, 3, 4}, {}], [[5, 1, 2, 3, 4], {3}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {2, 3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 774, 3353, 15390, 74337, 375867, 1981079, 10847572, 61533563, 360765180, 2181768006, 13587012532, 87001831088, 572082319503, 3858478155632] "" "Class ", 6640, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 746, 3094, 13371, 59873, 276670, 1315254, 6416483, 32058125, 163752469, 853905967, 4539986433, 24583331287, 135439367666, 758561402406] "" "Class ", 6641, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 5, 4], [1, 0, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 746, 3094, 13371, 59873, 276670, 1315254, 6416483, 32058125, 163752469, 853905967, 4539986433, 24583331287, 135439367666, 758561402406] "" "Class ", 6642, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 5, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 0, 1, 1]]} "Class ", 6643, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 2, 3, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 5, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[4, 5, 2, 3, 1], [1, 0, 1, 1]]} "Class ", 6644, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 5, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]} "Class ", 6645, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 5, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 4, 1, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 5, 2, 3, 1], [1, 1, 1, 1]]} "Class ", 6646, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {1, 3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {}], [[4, 2, 3, 1, 5], {1, 2, 3}, {}], [[5, 2, 3, 1, 4], {1, 2, 3}, {}], [[5, 2, 4, 1, 3], {1, 2}, {}], [[5, 3, 4, 1, 2], {1, 2}, {}], [[5, 3, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 819, 3793, 19057, 102990, 594763, 3650221, 23696585, 162071048, 1163812883, 8748156489, 68652848029, 561165567006, 4767646856199, 42022286055401] "" "Class ", 6647, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {1, 3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 768, 3363, 15909, 80896, 439760, 2543104, 15576169, 100646562, 683715476, 4868240105, 36234694627, 281252008058, 2271718326155, 19057344572673] "" "Class ", 6648, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]} "Class ", 6649, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4, 5], [0, 0, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {2}, {[0, 0, 0, 1]}], [[3, 2, 1], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [5, 4, 1, 3, 2], {1, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 733, 2991, 12736, 56606, 262815, 1274784, 6453820, 34043415, 186702844, 1062219931, 6256590855, 38083407344, 239176663219, 1547653554369] "" "Class ", 6650, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4, 5], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {}], [[4, 2, 3, 1, 5], {2, 3}, {}], [[5, 2, 3, 1, 4], {2, 3}, {}], [[5, 2, 4, 1, 3], {2, 3}, {}], [[5, 3, 4, 1, 2], {2, 3}, {}], [[5, 3, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 793, 3569, 17383, 91017, 509294, 3029960, 19081023, 126702411, 884126858, 6463855134, 49381308424, 393276187707, 3258158169194, 28025395373787] "" "Class ", 6651, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4, 5], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 733, 2990, 12711, 56245, 258841, 1237546, 6138785, 31547846, 167732789, 921434619, 5223792251, 30527332036, 183698380677, 1137081921786] "" "Class ", 6652, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 1, 0]]} "Class ", 6653, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 1, 0]]} "Class ", 6654, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {}], [[4, 2, 3, 1, 5], {1, 2, 3}, {}], [[5, 2, 3, 1, 4], {2, 3}, {}], [[5, 2, 4, 1, 3], {2, 3}, {}], [[5, 3, 4, 1, 2], {2, 3}, {}], [[5, 3, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 793, 3569, 17383, 91017, 509294, 3029960, 19081023, 126702411, 884126858, 6463855134, 49381308424, 393276187707, 3258158169194, 28025395373787] "" "Class ", 6655, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 733, 2990, 12711, 56245, 258841, 1237546, 6138785, 31547846, 167732789, 921434619, 5223792251, 30527332036, 183698380677, 1137081921786] "" "Class ", 6656, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 0, 0, 1]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [5, 3, 4, 1, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0]}], [ [5, 3, 4, 2, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 765, 3309, 15311, 75471, 394667, 2180854, 12687070, 77443458, 494547638, 3295275794, 22857305753, 164705084124, 1230636295559, 9518410705976] "" "Class ", 6657, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4, 5], [1, 0, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {2}, {[0, 0, 0, 1]}], [[3, 2, 1], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 187, 715, 2795, 11051, 43947, 175275, 700075, 2798251, 11188907, 44747435, 178973355, 715860651, 2863377067, 11453377195, 45813246635] "" "Class ", 6658, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4, 5], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {}], [[4, 2, 3, 1, 5], {2, 3}, {}], [[5, 2, 3, 1, 4], {2, 3}, {}], [[5, 2, 4, 1, 3], {2, 3}, {}], [[5, 3, 4, 1, 2], {2, 3}, {}], [[5, 3, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 793, 3569, 17383, 91017, 509294, 3029960, 19081023, 126702411, 884126858, 6463855134, 49381308424, 393276187707, 3258158169194, 28025395373787] "" "Class ", 6659, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4, 5], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 733, 2990, 12711, 56245, 258841, 1237546, 6138785, 31547846, 167732789, 921434619, 5223792251, 30527332036, 183698380677, 1137081921786] "" "Class ", 6660, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [0, 1, 1, 1]]} "Class ", 6661, " is:" {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4, 5], [1, 1, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 4, 2, 3, 1], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {2}, {[0, 0, 0, 1]}], [[3, 2, 1], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 187, 715, 2795, 11051, 43947, 175275, 700075, 2798251, 11188907, 44747435, 178973355, 715860651, 2863377067, 11453377195, 45813246635] "" "Class ", 6662, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 4, 3], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 4, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {1}, {}], [[4, 3, 1, 2, 5], {1, 2, 4}, {}], [[5, 3, 1, 2, 4], {1, 2, 4}, {}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 197, 846, 3976, 20240, 110711, 646444, 4007468, 26256229, 181106595, 1310753006, 9924791915, 78418066322, 645075207637, 5513333552793, 48868263437573] "" "Class ", 6663, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 4, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 4, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {[0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 835, 3890, 19629, 106452, 616472, 3791796, 24659242, 168900067, 1214316510, 9137034026, 71766127331, 587042499374, 4990631463307, 44011586928717] "" "Class ", 6664, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 2, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 4, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 4, 5, 2, 1], [0, 1, 0, 0]]} "Class ", 6665, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 2, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 4, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 4, 5, 2, 1], [1, 1, 0, 0]]} "Class ", 6666, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {3}, {}], [[3, 2, 1, 4, 5], {4}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 3, 5], {4}, {}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 2, 5], {4}, {}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {3, 4}, {}], [[5, 2, 1, 3, 4], {4}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {4}, {}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {3, 4}, {}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 799, 3581, 17225, 88353, 480705, 2762125, 16699561, 105896837, 702375905, 4860713661, 35020702065, 262175127733, 2035771570009, 16369545462221] "" "Class ", 6667, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {[0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [[3, 2, 1, 4, 5], {4}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 3, 5], {4}, {}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 2, 5], {4}, {[0, 0, 1, 0, 0, 0]}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {3, 4}, {}], [[5, 2, 1, 3, 4], {4}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {4}, {[0, 0, 1, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {3, 4}, {}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 3}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 787, 3474, 16385, 82086, 434787, 2425495, 14204293, 87075908, 557370385, 3716917695, 25771442227, 185446213578, 1382608160683, 10664068755489] "" "Class ", 6668, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 2, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 4, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 2, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 4, 3], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {3}, {}], [[3, 2, 1, 4, 5], {4}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 3, 5], {4}, {}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 2, 5], {4}, {}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {3, 4}, {}], [[5, 2, 1, 3, 4], {4}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {4}, {}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {3, 4}, {}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 799, 3581, 17225, 88353, 480705, 2762125, 16699561, 105896837, 702375905, 4860713661, 35020702065, 262175127733, 2035771570009, 16369545462221] "" "Class ", 6669, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 2, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 4, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 2, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 4, 3], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {[0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [[3, 2, 1, 4, 5], {4}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 3, 5], {4}, {}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 2, 5], {4}, {[0, 0, 1, 0, 0, 0]}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {3, 4}, {}], [[5, 2, 1, 3, 4], {4}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {4}, {[0, 0, 1, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {3, 4}, {}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 3}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 787, 3474, 16385, 82086, 434787, 2425495, 14204293, 87075908, 557370385, 3716917695, 25771442227, 185446213578, 1382608160683, 10664068755489] "" "Class ", 6670, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 4, 3], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 4, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {2}, {}], [[4, 3, 1, 2, 5], {1, 2, 4}, {}], [[5, 3, 1, 2, 4], {2, 4}, {}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 809, 3653, 17693, 91260, 498451, 2869128, 17334917, 109559444, 722188348, 4952293577, 35247993733, 259873885754, 1981125532727, 15591281667940] "" "Class ", 6671, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {[0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 795, 3521, 16595, 82648, 432499, 2367759, 13512639, 80152403, 492937342, 3136524383, 20610768119, 139647810352, 974214588259, 6988880351167] "" "Class ", 6672, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 2, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 4, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 4, 5, 2, 1], [0, 1, 0, 1]]} "Class ", 6673, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 2, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 4, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 4, 5, 2, 1], [1, 1, 0, 1]]} "Class ", 6674, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 2, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[3, 4, 5, 2, 1], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 2, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[3, 4, 5, 2, 1], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {4}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 2, 5, 4, 3], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 3, 5, 4, 2], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [2, 3, 5, 4, 1], {3, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0]}], [ [2, 4, 5, 3, 1], {4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 771, 3310, 14969, 70831, 348887, 1781732, 9403527, 51153208, 286163108, 1643164486, 9668406453, 58211101869, 358161052612, 2249461755186] "" "Class ", 6675, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 2, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 2, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {}, {}], [[3, 2, 4, 1], {}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {[0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [[3, 1, 2, 4, 5], {4}, {}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 4, 5], {4}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 4, 1, 5], {3}, {}], [[3, 2, 5, 1, 4], {1, 2}, {}], [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 3, 5, 1], {2}, {}], [[4, 2, 5, 1, 3], {1, 2}, {}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {3}, {}], [[4, 3, 5, 1, 2], {1, 2}, {[0, 0, 1, 0, 0, 0]}], [[4, 3, 5, 2, 1], {4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 757, 3174, 13852, 62441, 289102, 1369091, 6610013, 32452070, 161676944, 815973689, 4165888469, 21489245902, 111885361017, 587466883476] "" "Class ", 6676, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 2, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 4, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 4, 5, 2, 1], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 2, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 4, 3], [1, 1, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[3, 4, 5, 2, 1], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {4}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 2, 5, 4, 3], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 3, 5, 4, 2], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [2, 3, 5, 4, 1], {3, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0]}], [ [2, 4, 5, 3, 1], {4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 771, 3310, 14969, 70831, 348887, 1781732, 9403527, 51153208, 286163108, 1643164486, 9668406453, 58211101869, 358161052612, 2249461755186] "" "Class ", 6677, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 4, 5, 2, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 4, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 4, 5, 2, 1], [1, 1, 1, 1]]} "Class ", 6678, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 3, 5, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 3, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 3, 5, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 3, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 865, 4041, 20421, 110819, 641847, 3947116, 25659116, 175655664, 1262117329, 9490480133, 74491531316, 608915861899, 5173017570229, 45588946063127] "" "Class ", 6679, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 3, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 3, 5, 2, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1, 4, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 3, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 1, 3, 2], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 3, 5, 2, 1], [1, 1, 0, 0]]} "Class ", 6680, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 3, 5, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 3, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 3, 5, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 3, 4], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [[3, 2, 1, 4, 5], {4}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 3, 5], {4}, {}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {3, 4}, {}], [[5, 2, 1, 3, 4], {4}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 860, 3952, 19397, 100929, 553729, 3189991, 19234719, 121069949, 793718495, 5409112057, 38252200820, 280266354718, 2124422696960, 16637455794172] "" "Class ", 6681, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 3, 5, 2, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1, 4, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 3, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 3, 5, 2, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1, 4, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 3, 4], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [[3, 2, 1, 4, 5], {4}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 3, 5], {4}, {}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {3, 4}, {}], [[5, 2, 1, 3, 4], {4}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 860, 3952, 19397, 100929, 553729, 3189991, 19234719, 121069949, 793718495, 5409112057, 38252200820, 280266354718, 2124422696960, 16637455794172] "" "Class ", 6682, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 3, 5, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 3, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 3, 5, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 3, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 862, 3986, 19766, 104254, 581107, 3405504, 20895891, 133780762, 891067184, 6159184166, 44084779556, 326122573867, 2489255314534, 19575065403999] "" "Class ", 6683, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 3, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 3, 5, 2, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1, 4, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 3, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 1, 3, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 3, 5, 2, 1], [1, 1, 0, 1]]} "Class ", 6684, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 3, 5, 2, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1, 4, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 3, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 3, 5, 2, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1, 4, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 3, 4], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {}, {}], [[3, 2, 4, 1], {}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [[3, 1, 2, 4, 5], {4}, {}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 4, 5], {4}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 4, 1, 5], {3}, {}], [[3, 2, 5, 1, 4], {1, 2}, {}], [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 3, 5, 1], {2}, {}], [[4, 2, 5, 1, 3], {1, 2}, {}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {3}, {}], [[4, 3, 5, 1, 2], {4}, {[0, 1, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 52, 202, 858, 3908, 18801, 94448, 491234, 2628572, 14402157, 80508410, 457867056, 2643332641, 15462982142, 91520288748, 547374482632, 3304750155480] "" "Class ", 6685, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 1, 3, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 3, 5, 2, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1, 4, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 5, 3, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 1, 3, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 3, 5, 2, 1], [1, 1, 1, 1]]} "Class ", 6686, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {}, {}], [[4, 3, 2, 1, 5], {1, 2, 3}, {}], [[5, 3, 2, 1, 4], {1, 2, 3}, {}], [[5, 4, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {1, 2, 3}, {}], [[5, 4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 197, 846, 3976, 20240, 110711, 646444, 4007468, 26256229, 181106595, 1310753006, 9924791915, 78418066322, 645075207637, 5513333552793, 48868263437573] "" "Class ", 6687, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 828, 3850, 19401, 105124, 608484, 3741776, 24332292, 166669641, 1198450885, 9019500898, 70860630641, 579798251781, 4930536134137, 43495393609651] "" "Class ", 6688, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 4, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 5, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 1, 0, 0]]} "Class ", 6689, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 2, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 4, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 5, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 2, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 4, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 5, 3], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {}, {}], [[4, 2, 1, 3], {}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {1}, {[0, 0, 1, 0, 0]}], [[3, 2, 1, 4, 5], {4}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 3, 5], {4}, {}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 2, 5], {4}, {}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}], [[5, 2, 1, 3, 4], {4}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {4}, {}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}], [[5, 4, 1, 2, 3], {4}, {}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 782, 3486, 16826, 87397, 485692, 2872926, 18005325, 119082057, 828188008, 6038087403, 46021729198, 365810296063, 3025703092485, 25990664318707] "" "Class ", 6690, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {}, {}], [[3, 2, 1, 4, 5], {4}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 3, 5], {4}, {}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 2, 5], {4}, {}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 1, 5], {3}, {}], [[4, 3, 2, 5, 1], {3, 4}, {}], [[5, 2, 1, 3, 4], {4}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {4}, {}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {3}, {}], [[5, 3, 2, 4, 1], {3, 4}, {}], [[5, 4, 1, 2, 3], {4}, {}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {3}, {}], [[5, 4, 3, 1, 2], {3}, {}], [[5, 4, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 804, 3649, 17893, 94145, 528422, 3148330, 19826647, 131487973, 915352068, 6669893832, 50743407551, 402149795201, 3313293891345, 28326765522153] "" "Class ", 6691, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {1}, {[0, 0, 1, 0, 0]}], [[3, 2, 1, 4, 5], {4}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 3, 5], {4}, {}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 2, 5], {4}, {}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {3, 4}, {}], [[5, 2, 1, 3, 4], {4}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {4}, {}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {3, 4}, {}], [[5, 4, 1, 2, 3], {4}, {}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 3}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 790, 3518, 16826, 85920, 466161, 2676229, 16199824, 103072487, 687421088, 4793812317, 34878273722, 264224951933, 2080392956528, 16995956202977] "" "Class ", 6692, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 4, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 5, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 1, 1, 0]]} "Class ", 6693, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 2, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 4, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 5, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 5, 4, 2, 1], [1, 1, 1, 0]]} "Class ", 6694, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {}, {}], [[4, 3, 2, 1, 5], {1, 2, 3}, {}], [[5, 3, 2, 1, 4], {2, 3}, {}], [[5, 4, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {2, 3}, {}], [[5, 4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 824, 3802, 18975, 101669, 581281, 3528161, 22634908, 152912577, 1084225040, 8045584570, 62323318100, 502817692389, 4216486824800, 36683478703992] "" "Class ", 6695, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 802, 3621, 17627, 91954, 511458, 3020074, 18860083, 124141531, 858645141, 6223486480, 47150519823, 372544408192, 3063382837283, 26165367728385] "" "Class ", 6696, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 4, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 5, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 1, 0, 1]]} "Class ", 6697, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 2, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 4, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 5, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 2, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 4, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 5, 3], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[3, 2, 1, 4], {}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {2}, {[0, 0, 1, 0, 0]}], [[3, 2, 1, 4, 5], {4}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 3, 5], {4}, {}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 2, 5], {4}, {}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}], [[5, 2, 1, 3, 4], {4}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {4}, {}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {2, 3}, {[0, 0, 1, 0, 0, 0]}], [[5, 4, 1, 2, 3], {4}, {}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 748, 3127, 13708, 62659, 297320, 1459618, 7395420, 38602205, 207297259, 1144037578, 6482983276, 37695269777, 224758353401, 1373528543980] "" "Class ", 6698, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 4, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 5, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 4, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 5, 3], [1, 1, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {3}, {[0, 0, 0, 0, 0, 1]}], [[1, 5, 2, 4, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [2, 5, 3, 4, 1], {3, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 790, 3519, 16853, 86300, 470304, 2716450, 16569455, 106388473, 716968177, 5058096289, 37267234198, 286144641874, 2285131434445, 18946369356568] "" "Class ", 6699, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 4, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[3, 5, 4, 2, 1], [1, 0, 1, 1]]} "Class ", 6700, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 4, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 5, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[3, 5, 4, 2, 1], [0, 1, 1, 1]]} "Class ", 6701, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 5, 4, 2, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2, 4, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 5, 3], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 2, 1, 3], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[3, 5, 4, 2, 1], [1, 1, 1, 1]]} "Class ", 6702, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {1}, {}], [[4, 3, 1, 2, 5], {1, 2, 4}, {}], [[5, 3, 1, 2, 4], {1, 2, 4}, {}], [[5, 4, 1, 2, 3], {1, 2, 4}, {}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 831, 3891, 19767, 107967, 629739, 3900807, 25542231, 176100831, 1274060979, 9644151027, 76182561255, 626563053447, 5354240030415, 47451595373127] "" "Class ", 6703, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {[1, 0, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 796, 3619, 17920, 95862, 549797, 3358749, 21738478, 148392841, 1064372308, 7996006960, 62739296841, 512895972808, 4359125074823, 38442121302952] "" "Class ", 6704, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 1, 0, 0]]} "Class ", 6705, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 0, 0]]} "Class ", 6706, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3, 5], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {3}, {}], [[3, 2, 1, 4, 5], {4}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 3, 5], {4}, {}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 2, 5], {4}, {}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {3, 4}, {}], [[5, 2, 1, 3, 4], {4}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {4}, {}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {3, 4}, {}], [[5, 4, 1, 2, 3], {4}, {}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 781, 3469, 16631, 85491, 468537, 2724833, 16747171, 108389911, 736382213, 5236791237, 38885666991, 300817541531, 2419516810609, 20196271982281] "" "Class ", 6707, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {[1, 0, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [[3, 2, 1, 4, 5], {4}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 3, 5], {4}, {}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 2, 5], {4}, {[1, 0, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {3, 4}, {}], [[5, 2, 1, 3, 4], {4}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {4}, {[1, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {3, 4}, {}], [[5, 4, 1, 2, 3], {3}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 749, 3149, 13997, 65637, 324093, 1681557, 9148685, 52083509, 309639629, 1918634805, 12368650701, 82815657525, 575014148813, 4134126910517] "" "Class ", 6708, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3, 5], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {3}, {}], [[3, 2, 1, 4, 5], {4}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 3, 5], {4}, {}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 2, 5], {4}, {}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {3, 4}, {}], [[5, 2, 1, 3, 4], {4}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {4}, {}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {3, 4}, {}], [[5, 4, 1, 2, 3], {4}, {}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 781, 3469, 16631, 85491, 468537, 2724833, 16747171, 108389911, 736382213, 5236791237, 38885666991, 300817541531, 2419516810609, 20196271982281] "" "Class ", 6709, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3, 5], [0, 1, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 0, 0, 1]}], [[4, 1, 3, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 3, 4, 1, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 3, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 749, 3149, 13997, 65637, 324093, 1681557, 9148685, 52083509, 309639629, 1918634805, 12368650701, 82815657525, 575014148813, 4134126910517] "" "Class ", 6710, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {2}, {}], [[4, 3, 1, 2, 5], {1, 2, 4}, {}], [[5, 3, 1, 2, 4], {2, 4}, {}], [[5, 4, 1, 2, 3], {2, 4}, {}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 806, 3671, 18050, 95135, 534473, 3184900, 20045913, 132788053, 922856421, 6710369933, 50924335897, 402451573821, 3305591194985, 28167682839069] "" "Class ", 6711, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {1, 2}, {[1, 0, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 764, 3289, 15061, 72934, 371636, 1984435, 11067131, 64282626, 387932953, 2427121093, 15713307227, 105085735926, 724862207712, 5149957029353] "" "Class ", 6712, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 1, 0, 1]]} "Class ", 6713, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 0, 1]]} "Class ", 6714, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3, 5], [1, 1, 0, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 0, 0, 1]}], [[4, 1, 3, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[4, 1, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [5, 1, 4, 3, 2], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0]}], [ [5, 2, 4, 3, 1], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {4}, { [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 764, 3288, 15043, 72745, 370099, 1973584, 10996665, 63849977, 385410533, 2413453066, 15649413365, 104900449698, 725810507872, 5176569085801] "" "Class ", 6715, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 0, 0, 1]}], [[4, 1, 3, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 731, 2950, 12235, 51822, 223191, 974427, 4302645, 19181100, 86211885, 390248055, 1777495635, 8140539950, 37463689775, 173164232965] "" "Class ", 6716, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3, 5], [1, 1, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 0, 0, 1]}], [[4, 1, 3, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[4, 1, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [5, 1, 4, 3, 2], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0]}], [ [5, 2, 4, 3, 1], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {4}, { [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 190, 764, 3288, 15043, 72745, 370099, 1973584, 10996665, 63849977, 385410533, 2413453066, 15649413365, 104900449698, 725810507872, 5176569085801] "" "Class ", 6717, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 2, 3, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3, 5], [1, 1, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 0, 0, 1]}], [[4, 1, 3, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 731, 2950, 12235, 51822, 223191, 974427, 4302645, 19181100, 86211885, 390248055, 1777495635, 8140539950, 37463689775, 173164232965] "" "Class ", 6718, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {}, {}], [[4, 3, 2, 1, 5], {1, 2, 3}, {}], [[5, 3, 2, 1, 4], {1, 2, 3}, {}], [[5, 4, 2, 1, 3], {1, 2, 3}, {}], [[5, 4, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 839, 3937, 20022, 109441, 638704, 3958034, 25925188, 178784770, 1293728539, 9794544676, 77380315154, 636479868900, 5439451892986, 48210270580437] "" "Class ", 6719, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 828, 3850, 19401, 105124, 608484, 3741776, 24332292, 166669641, 1198450885, 9019500898, 70860630641, 579798251781, 4930536134137, 43495393609651] "" "Class ", 6720, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 5, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 5, 4], [0, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 5, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 791, 3535, 17015, 87692, 481557, 2805881, 17283249, 112175572, 764926481, 5465708993, 40826469931, 318097406162, 2580093213099, 21745610715297] "" "Class ", 6721, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 2, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 5, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 2, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 5, 4], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {}, {}], [[4, 2, 1, 3], {}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {1}, {[0, 1, 0, 0, 0]}], [[3, 2, 1, 4, 5], {4}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 3, 5], {4}, {}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 2, 5], {4}, {}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {1, 4}, {[0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 3, 4], {4}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {4}, {}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {1, 4}, {[0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {4}, {}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 3}, {[0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 791, 3535, 17015, 87692, 481557, 2805881, 17283249, 112175572, 764926481, 5465708993, 40826469931, 318097406162, 2580093213099, 21745610715297] "" "Class ", 6722, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {}, {}], [[3, 2, 1, 4, 5], {4}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 3, 5], {4}, {}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 2, 5], {4}, {}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 1, 5], {3}, {}], [[4, 3, 2, 5, 1], {3, 4}, {}], [[5, 2, 1, 3, 4], {4}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {4}, {}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {3}, {}], [[5, 3, 2, 4, 1], {3, 4}, {}], [[5, 4, 1, 2, 3], {4}, {}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {3}, {}], [[5, 4, 2, 3, 1], {3}, {}], [[5, 4, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 795, 3597, 17628, 92792, 521179, 3107266, 19579112, 129891327, 904269342, 6587000687, 50077609679, 396444004276, 3261522182135, 27833208714875] "" "Class ", 6723, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {3}, {[0, 1, 0, 0, 0]}], [[3, 2, 1, 4, 5], {4}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 3, 5], {4}, {}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 2, 5], {4}, {}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {3, 4}, {}], [[5, 2, 1, 3, 4], {4}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {4}, {}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {3, 4}, {}], [[5, 4, 1, 2, 3], {4}, {}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 781, 3467, 16593, 85047, 464273, 2687147, 16424261, 105640499, 712827161, 5032280895, 37078273065, 284513690771, 2269152080749, 18777106710059] "" "Class ", 6724, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 5, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 0]]} "Class ", 6725, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 2, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 5, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 5, 3, 2, 1], [1, 1, 1, 0]]} "Class ", 6726, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {}, {}], [[4, 3, 2, 1, 5], {1, 2, 3}, {}], [[5, 3, 2, 1, 4], {2, 3}, {}], [[5, 4, 2, 1, 3], {2, 3}, {}], [[5, 4, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 828, 3853, 19442, 105506, 611672, 3767648, 24542311, 168396558, 1212935545, 9143920787, 71957453717, 589731775211, 5022999722058, 44380000283101] "" "Class ", 6727, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 194, 816, 3750, 18653, 99678, 568699, 3446058, 22079333, 149008121, 1055720700, 7829512185, 60624018772, 488966612356, 4099600546998, 35663428860038] "" "Class ", 6728, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1], {3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 777, 3402, 15917, 79127, 416029, 2304561, 13405525, 81650002, 519394953, 3442883555, 23732604255, 169811800071, 1259110554053, 9659859502082] "" "Class ", 6729, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 2, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 5, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 2, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 5, 4], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[3, 2, 1, 4], {}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {1}, {[0, 1, 0, 0, 0]}], [[3, 2, 1, 4, 5], {4}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 3, 5], {4}, {}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 2, 5], {4}, {}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {1, 4}, {[0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 3, 4], {4}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {4}, {}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {1, 4}, {[0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {4}, {}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 3}, {[0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 777, 3402, 15917, 79127, 416029, 2304561, 13405525, 81650002, 519394953, 3442883555, 23732604255, 169811800071, 1259110554053, 9659859502082] "" "Class ", 6730, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 5, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 1]]} "Class ", 6731, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 5, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 1]]} "Class ", 6732, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 5, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]} "Class ", 6733, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[4, 5, 3, 2, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 5, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[4, 5, 3, 2, 1], [1, 1, 1, 1]]} "Class ", 6734, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {}, {}], [[4, 3, 2, 1, 5], {1, 2, 3}, {}], [[5, 3, 2, 1, 4], {1, 2, 3}, {}], [[5, 4, 2, 1, 3], {1, 2, 3}, {}], [[5, 4, 3, 1, 2], {1, 2, 3}, {}], [[5, 4, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 196, 840, 3946, 20078, 109771, 640720, 3970946, 26011671, 179390200, 1298156800, 9828340096, 77648948925, 638699938419, 5458495400894, 48379554136419] "" "Class ", 6735, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 797, 3633, 18042, 96748, 555831, 3399554, 22020027, 150398714, 1079197932, 8109851620, 63647472488, 520416314225, 4423694667257, 39016239031735] "" "Class ", 6736, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 0, 0, 1]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 2, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 3, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [5, 3, 4, 2, 1], {2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 4, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {1, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 4, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 192, 794, 3581, 17475, 91614, 512922, 3051365, 19204133, 127380346, 887511746, 6476474963, 49370545321, 392241674034, 3241084423904, 27800951063259] "" "Class ", 6737, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4, 5], [0, 0, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {2}, {[0, 0, 0, 1]}], [[3, 2, 1], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 2, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {1, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 4, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 751, 3191, 14533, 71103, 373643, 2103401, 12631947, 80548671, 542887793, 3851676291, 28663604107, 223056882285, 1810267245815, 15286018639599] "" "Class ", 6738, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {}, {}], [[3, 2, 1, 4, 5], {4}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 3, 5], {4}, {}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 2, 5], {4}, {}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 1, 5], {3}, {}], [[4, 3, 2, 5, 1], {3, 4}, {}], [[5, 2, 1, 3, 4], {4}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {4}, {}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {3}, {}], [[5, 3, 2, 4, 1], {3, 4}, {}], [[5, 4, 1, 2, 3], {4}, {}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {3}, {}], [[5, 4, 2, 3, 1], {3}, {}], [[5, 4, 3, 1, 2], {3}, {}], [[5, 4, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 193, 807, 3697, 18383, 98391, 563005, 3425023, 22047999, 149583559, 1065857955, 7952440381, 61962608585, 502990801157, 4244959584603, 37174474266497] "" "Class ", 6739, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}], [[3, 2, 1, 4, 5], {4}, {}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 3, 5], {4}, {}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 2, 5], {4}, {}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {3, 4}, {}], [[5, 2, 1, 3, 4], {4}, {}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {4}, {}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {3, 4}, {}], [[5, 4, 1, 2, 3], {4}, {}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3, 4}, {[1, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 189, 751, 3189, 14483, 70365, 365127, 2017413, 11825275, 73260381, 478012943, 3274408677, 23480331747, 175809954717, 1371380993239, 11121334026501] "" "Class ", 6740, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 0]]} "Class ", 6741, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {2}, {[0, 0, 0, 1]}], [[3, 2, 1], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 2, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 4, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 187, 715, 2795, 11051, 43947, 175275, 700075, 2798251, 11188907, 44747435, 178973355, 715860651, 2863377067, 11453377195, 45813246635] "" "Class ", 6742, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {}, {}], [[4, 3, 2, 1, 5], {1, 2, 3}, {}], [[5, 3, 2, 1, 4], {2, 3}, {}], [[5, 4, 2, 1, 3], {2, 3}, {}], [[5, 4, 3, 1, 2], {2, 3}, {}], [[5, 4, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 195, 829, 3862, 19501, 105876, 614039, 3783294, 24649636, 169162306, 1218621400, 9187833568, 72309842823, 592666460995, 5048330625182, 44606323292920] "" "Class ", 6743, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 781, 3473, 16715, 86563, 479589, 2827849, 17665299, 116450867, 807253517, 5866610905, 44574763131, 353229661043, 2913014995157, 24951144008521] "" "Class ", 6744, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}], [[3, 2, 1], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 0, 0, 1]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 2, 1], {1, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[5, 3, 4, 1, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [5, 3, 4, 2, 1], {1, 2, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 191, 780, 3452, 16453, 83965, 456559, 2633977, 16062648, 103192220, 696275753, 4920733359, 36334220791, 279680380363, 2239644339224, 18623278057752] "" "Class ", 6745, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {2}, {[0, 0, 0, 1]}], [[3, 2, 1], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 2, 1], {1, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 188, 733, 2990, 12711, 56245, 258841, 1237546, 6138785, 31547846, 167732789, 921434619, 5223792251, 30527332036, 183698380677, 1137081921786] "" "Class ", 6746, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]} "Class ", 6747, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]} "Class ", 6748, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]} "Class ", 6749, " is:" {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]} {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [0, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {2}, {[0, 0, 0, 1]}], [[3, 2, 1], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 2, 1], {4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 15, 51, 187, 715, 2795, 11051, 43947, 175275, 700075, 2798251, 11188907, 44747435, 178973355, 715860651, 2863377067, 11453377195, 45813246635] "" "Class ", 6750, " is:" {{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 5, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1265, 4147, 13798, 46476, 158170, 543050, 1878670, 6542330, 22915999, 80682987, 285378270, 1013564805, 3613262795] "" "Class ", 6751, " is:" {{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1210, 3865, 12482, 40677, 133572, 441468, 1467296, 4900760, 16439370, 55357305, 187050302, 633998079, 2154950454] "" "Class ", 6752, " is:" {{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]} "Class ", 6753, " is:" {{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 2], [0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 6754, " is:" {{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[1, 2, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 5, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1221, 3939, 12886, 42648, 142544, 480459, 1631287, 5574073, 19153815, 66146259, 229452587, 799140681, 2793373937] "" "Class ", 6755, " is:" {{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [ [1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 6756, " is:" {{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 1, 0]]} "Class ", 6757, " is:" {{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 2], [0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [ [2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 2], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6758, " is:" {{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 5, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1265, 4147, 13798, 46476, 158170, 543050, 1878670, 6542330, 22915999, 80682987, 285378270, 1013564805, 3613262795] "" "Class ", 6759, " is:" {{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1210, 3865, 12482, 40677, 133572, 441468, 1467296, 4900760, 16439370, 55357305, 187050302, 633998079, 2154950454] "" "Class ", 6760, " is:" {{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]} "Class ", 6761, " is:" {{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 2], [0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 6762, " is:" {{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[1, 2, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 5, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1221, 3939, 12886, 42648, 142544, 480459, 1631287, 5574073, 19153815, 66146259, 229452587, 799140681, 2793373937] "" "Class ", 6763, " is:" {{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [ [1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 6764, " is:" {{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]} "Class ", 6765, " is:" {{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 2], [0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [ [2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 2], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6766, " is:" {{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 5, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 5, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 4, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1265, 4148, 13808, 46542, 158534, 544869, 1887212, 6580775, 23083823, 81399079, 288380766, 1025982051, 3664054185] "" "Class ", 6767, " is:" {{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 5, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 5, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1211, 3875, 12548, 41040, 135370, 449791, 1504057, 5057668, 17092030, 58018150, 197727023, 676290905, 2320721255] "" "Class ", 6768, " is:" {{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 5, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 2, 3, 5, 4], [0, 1, 0, 0]]} "Class ", 6769, " is:" {{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 5, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 5, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 2], [0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 6770, " is:" {{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 5, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 5, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 4, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1221, 3939, 12886, 42648, 142544, 480459, 1631287, 5574073, 19153815, 66146259, 229452587, 799140681, 2793373937] "" "Class ", 6771, " is:" {{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 6772, " is:" {{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 5, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 2, 3, 5, 4], [0, 1, 1, 0]]} "Class ", 6773, " is:" {{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 5, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 5, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 2], [0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6774, " is:" {{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 1]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]} "Class ", 6775, " is:" {{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 1]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]} "Class ", 6776, " is:" {{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]} "Class ", 6777, " is:" {{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 5, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 1]], [[1, 2, 3, 5, 4], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 5, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [1, 1]], [[1, 2, 3, 5, 4], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[1, 2, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6778, " is:" {{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 5, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 5, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 4, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1221, 3939, 12886, 42648, 142544, 480459, 1631287, 5574073, 19153815, 66146259, 229452587, 799140681, 2793373937] "" "Class ", 6779, " is:" {{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 5, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 5, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 6780, " is:" {{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 5, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 2, 3, 5, 4], [0, 1, 1, 1]]} "Class ", 6781, " is:" {{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 5, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 3, 5, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 2], [0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6782, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 3, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 3, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 3, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 3, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4157, 13863, 46827, 159886, 550943, 1913526, 6691891, 23544320, 83280751, 295986327, 1056461081, 3785365874] "" "Class ", 6783, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 3, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 3, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 3, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 3, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [ [2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1220, 3929, 12822, 42309, 140922, 473169, 1599864, 5442561, 18615176, 63975857, 220816906, 765121477, 2660426630] "" "Class ", 6784, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 3, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 3, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 3, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 3, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1158, 3615, 11393, 36209, 115940, 373709, 1211740, 3949969, 12937612, 42558745, 140547051, 465799527, 1548766044] "" "Class ", 6785, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 3, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 3, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 3, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 3, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 2], [0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6786, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 3, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 3, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 1]], [[1, 2, 5, 3, 4], [0, 0, 1, 0]]} "Class ", 6787, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 3, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 3, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 1]], [[1, 2, 5, 3, 4], [1, 0, 1, 0]]} "Class ", 6788, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 3, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 3, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 3, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 3, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1158, 3615, 11393, 36209, 115940, 373709, 1211740, 3949969, 12937612, 42558745, 140547051, 465799527, 1548766044] "" "Class ", 6789, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 3, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 3, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 2], [0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6790, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 3, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 3, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4157, 13863, 46827, 159886, 550943, 1913526, 6691891, 23544320, 83280751, 295986327, 1056461081, 3785365874] "" "Class ", 6791, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 3, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 3, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [ [2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1220, 3929, 12822, 42309, 140922, 473169, 1599864, 5442561, 18615176, 63975857, 220816906, 765121477, 2660426630] "" "Class ", 6792, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 3, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 3, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1158, 3615, 11393, 36209, 115940, 373709, 1211740, 3949969, 12937612, 42558745, 140547051, 465799527, 1548766044] "" "Class ", 6793, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 3, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 3, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 2], [0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6794, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 3, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 3, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 1]], [[1, 2, 5, 3, 4], [0, 0, 1, 1]]} "Class ", 6795, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 3, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 3, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 1]], [[1, 2, 5, 3, 4], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 3, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 3, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 1, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [1, 1]], [[1, 2, 5, 3, 4], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6796, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 3, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 3, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1158, 3615, 11393, 36209, 115940, 373709, 1211740, 3949969, 12937612, 42558745, 140547051, 465799527, 1548766044] "" "Class ", 6797, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 3, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 3, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 3, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 3, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4157, 13863, 46827, 159886, 550943, 1913526, 6691891, 23544320, 83280751, 295986327, 1056461081, 3785365874] "" "Class ", 6798, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 3, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 3, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 3, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 3, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 6799, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 3, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 3, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 5, 2, 3, 4], [0, 1, 0, 0]]} "Class ", 6800, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 3, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 3, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 6801, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 3, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 3, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 3, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 3, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {1, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 386, 1231, 4003, 13224, 44259, 149762, 511515, 1761202, 6106589, 21303654, 74725120, 263376981, 932329208, 3313255227] "" "Class ", 6802, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 3, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 3, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 3, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 3, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6803, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 3, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 3, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 5, 2, 3, 4], [0, 1, 1, 0]]} "Class ", 6804, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 3, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 3, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 3, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 3, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6805, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 3, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 3, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 5, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 3, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 3, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 5, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4157, 13863, 46827, 159886, 550943, 1913526, 6691891, 23544320, 83280751, 295986327, 1056461081, 3785365874] "" "Class ", 6806, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 3, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 3, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 5, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 3, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 3, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 5, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 6807, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 3, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 3, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 5, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 5, 2, 3, 4], [0, 1, 0, 1]]} "Class ", 6808, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 3, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 5, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 3, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 5, 1], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 6809, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 3, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 3, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 5, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 3, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 3, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 5, 1], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {1, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 386, 1231, 4003, 13224, 44259, 149762, 511515, 1761202, 6106589, 21303654, 74725120, 263376981, 932329208, 3313255227] "" "Class ", 6810, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 3, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 3, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 5, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 3, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 3, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 5, 1], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6811, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 3, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 3, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 5, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 5, 2, 3, 4], [0, 1, 1, 1]]} "Class ", 6812, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [ [1, 2, 3, 4, 5], {1}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1210, 3865, 12482, 40677, 133572, 441468, 1467296, 4900760, 16439370, 55357305, 187050302, 633998079, 2154950454] "" "Class ", 6813, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1210, 3865, 12482, 40677, 133572, 441468, 1467296, 4900760, 16439370, 55357305, 187050302, 633998079, 2154950454] "" "Class ", 6814, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 3, 4], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 3, 2], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[5, 1, 2, 3, 4], [0, 1, 0, 0]]} "Class ", 6815, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]} "Class ", 6816, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 3, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 3, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 3, 4], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 3, 2], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1, 5], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[1, 2, 3, 4, 5], {1}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 6817, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1, 5], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [ [1, 2, 3, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 6818, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 3, 4], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 3, 2], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[5, 1, 2, 3, 4], [0, 1, 1, 0]]} "Class ", 6819, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 0]]} "Class ", 6820, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [ [1, 2, 3, 4, 5], {1}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1210, 3865, 12482, 40677, 133572, 441468, 1467296, 4900760, 16439370, 55357305, 187050302, 633998079, 2154950454] "" "Class ", 6821, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1210, 3865, 12482, 40677, 133572, 441468, 1467296, 4900760, 16439370, 55357305, 187050302, 633998079, 2154950454] "" "Class ", 6822, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 3, 4], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 3, 2], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[5, 1, 2, 3, 4], [0, 1, 0, 1]]} "Class ", 6823, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]} "Class ", 6824, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 3, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 3, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 3, 4], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 3, 2], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1, 5], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[1, 2, 3, 4, 5], {1}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 6825, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1, 5], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [ [1, 2, 3, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 6826, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 3, 4], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 3, 2], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[5, 1, 2, 3, 4], [0, 1, 1, 1]]} "Class ", 6827, " is:" {{[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 4, 5, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 2, 1, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 5, 4, 2, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 4, 5, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 2, 1, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 5, 4, 2, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 1, 0, 0]}], [[3, 1, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 3, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 401, 1310, 4368, 14806, 50868, 176738, 619932, 2192288, 7807625, 27978530, 100809146, 364990184, 1327233335, 4845181810] "" "Class ", 6828, " is:" {{[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 4, 5, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 2, 1, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 5, 4, 2, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 4, 5, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 2, 1, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 5, 4, 2, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4158, 13873, 46893, 160247, 552723, 1921756, 6728347, 23701026, 83939765, 298712615, 1067598164, 3830414563] "" "Class ", 6829, " is:" {{[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 4, 5, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 5, 4, 2, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 2, 4, 5, 3], [0, 1, 0, 0]]} "Class ", 6830, " is:" {{[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 4, 5, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 5, 4, 2, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 4, 5, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 5, 4, 2, 1], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 0, 0, 2], [0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 6831, " is:" {{[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 4, 5, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 2, 1, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 5, 4, 2, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 1]], [[1, 2, 4, 5, 3], [0, 0, 1, 0]]} "Class ", 6832, " is:" {{[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 4, 5, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 2, 1, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 5, 4, 2, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 1]], [[1, 2, 4, 5, 3], [1, 0, 1, 0]]} "Class ", 6833, " is:" {{[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 4, 5, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 2, 1, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 5, 4, 2, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 2, 4, 5, 3], [0, 1, 1, 0]]} "Class ", 6834, " is:" {{[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 4, 5, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 2, 1, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 5, 4, 2, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 1]], [[1, 2, 4, 5, 3], [1, 1, 1, 0]]} "Class ", 6835, " is:" {{[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 5, 4, 2, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 1]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]} "Class ", 6836, " is:" {{[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 5, 4, 2, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 1]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]} "Class ", 6837, " is:" {{[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 5, 4, 2, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]} "Class ", 6838, " is:" {{[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 5, 4, 2, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 1]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 5, 4, 2, 1], [1, 0, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [1, 1]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[1, 2, 3, 4], {2}, {[0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6839, " is:" {{[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 4, 5, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 2, 1, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 5, 4, 2, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 1]], [[1, 2, 4, 5, 3], [0, 0, 1, 1]]} "Class ", 6840, " is:" {{[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 4, 5, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 2, 1, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 5, 4, 2, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 1]], [[1, 2, 4, 5, 3], [1, 0, 1, 1]]} "Class ", 6841, " is:" {{[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 4, 5, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 2, 1, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 5, 4, 2, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 2, 4, 5, 3], [0, 1, 1, 1]]} "Class ", 6842, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 4, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 2, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 4, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 2, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 401, 1310, 4368, 14806, 50868, 176738, 619932, 2192288, 7807625, 27978530, 100809146, 364990184, 1327233335, 4845181810] "" "Class ", 6843, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 4, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 2, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 4, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 2, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4158, 13873, 46893, 160247, 552723, 1921756, 6728347, 23701026, 83939765, 298712615, 1067598164, 3830414563] "" "Class ", 6844, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 4, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 2, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 4, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 2, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 3, 5], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 2, 5], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {1, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [ [5, 2, 1, 3, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 383, 1202, 3819, 12255, 39651, 129190, 423469, 1395425, 4619787, 15358681, 51253577, 171625635, 576499577, 1942062420] "" "Class ", 6845, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 4, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 4, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 0, 2]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 6846, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 4, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 2, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 1]], [[1, 2, 5, 4, 3], [0, 0, 1, 0]]} "Class ", 6847, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 4, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 2, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 1]], [[1, 2, 5, 4, 3], [1, 0, 1, 0]]} "Class ", 6848, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 4, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 2, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 4, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 2, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {1, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 367, 1117, 3441, 10720, 33727, 107012, 342023, 1100128, 3558535, 11568339, 37776029, 123855123, 407565811, 1345623584] "" "Class ", 6849, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 4, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 4, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 0, 2]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 356, 1044, 3057, 8948, 26192, 76674, 224465, 657137, 1923817, 5632105, 16488346, 48270655, 141315320, 413709331] "" "Class ", 6850, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 4, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 1]], [[1, 2, 5, 4, 3], [0, 0, 0, 1]]} "Class ", 6851, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 1]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]} "Class ", 6852, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 3, 5], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {1, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [ [5, 2, 1, 3, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1158, 3615, 11393, 36209, 115940, 373709, 1211740, 3949969, 12937612, 42558745, 140547051, 465799527, 1548766044] "" "Class ", 6853, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 0, 2]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6854, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 4, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 2, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 1]], [[1, 2, 5, 4, 3], [0, 0, 1, 1]]} "Class ", 6855, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 4, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 2, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 1]], [[1, 2, 5, 4, 3], [1, 0, 1, 1]]} "Class ", 6856, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 4, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 4, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {1, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 367, 1117, 3441, 10720, 33727, 107012, 342023, 1100128, 3558535, 11568339, 37776029, 123855123, 407565811, 1345623584] "" "Class ", 6857, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 4, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 4, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 0, 2]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 356, 1044, 3057, 8948, 26192, 76674, 224465, 657137, 1923817, 5632105, 16488346, 48270655, 141315320, 413709331] "" "Class ", 6858, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 4, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 2, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 4, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 2, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}] , [[4, 3, 5, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 402, 1317, 4403, 14963, 51537, 179503, 631144, 2237199, 7986056, 28683449, 103583004, 375874395, 1369853869, 5011826841] "" "Class ", 6859, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 4, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 2, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 4, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 2, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1221, 3939, 12885, 42636, 142456, 479944, 1628631, 5561411, 19096541, 65896618, 228393724, 794741412, 2775388162] "" "Class ", 6860, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 4, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 2, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 5, 2, 4, 3], [0, 1, 0, 0]]} "Class ", 6861, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 4, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 2, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 4, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 2, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 6862, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 4, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 2, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 4, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 2, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 1, 2], {1, 2, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 386, 1231, 4003, 13224, 44259, 149762, 511515, 1761202, 6106589, 21303654, 74725120, 263376981, 932329208, 3313255227] "" "Class ", 6863, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 4, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 2, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 4, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 2, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6864, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 4, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 2, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 5, 2, 4, 3], [0, 1, 1, 0]]} "Class ", 6865, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 4, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 2, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 4, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 2, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6866, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 4, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 2, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 1]], [[1, 5, 2, 4, 3], [0, 0, 0, 1]]} "Class ", 6867, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 4, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 2, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 1]], [[1, 5, 2, 4, 3], [1, 0, 0, 1]]} "Class ", 6868, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 4, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 2, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 5, 2, 4, 3], [0, 1, 0, 1]]} "Class ", 6869, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 4, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 2, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 1]], [[1, 5, 2, 4, 3], [1, 1, 0, 1]]} "Class ", 6870, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 4, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 2, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 4, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 2, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 1, 2], {1, 2, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 386, 1231, 4003, 13224, 44259, 149762, 511515, 1761202, 6106589, 21303654, 74725120, 263376981, 932329208, 3313255227] "" "Class ", 6871, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 4, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 2, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 4, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 2, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6872, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 4, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 2, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 5, 2, 4, 3], [0, 1, 1, 1]]} "Class ", 6873, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 4, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 2, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 1, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 4, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 2, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 1, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [ [2, 1, 3, 4, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 4, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4159, 13883, 46959, 160608, 554500, 1929947, 6764488, 23855708, 84587419, 301380544, 1078453368, 3874161462] "" "Class ", 6874, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 4, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 2, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 1, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 4, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 2, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 1, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1211, 3875, 12548, 41040, 135370, 449791, 1504057, 5057668, 17092030, 58018150, 197727023, 676290905, 2320721255] "" "Class ", 6875, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 4, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 2, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 1, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[5, 1, 2, 4, 3], [0, 1, 0, 0]]} "Class ", 6876, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 4, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 2, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 1, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 1]], [[5, 1, 2, 4, 3], [1, 1, 0, 0]]} "Class ", 6877, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 4, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 2, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 1, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 4, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 2, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 1, 5], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [ [2, 1, 3, 4, 5], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 4, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 6878, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 4, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 2, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 1, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 4, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 2, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 1, 5], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 6879, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 4, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 2, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 1, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[5, 1, 2, 4, 3], [0, 1, 1, 0]]} "Class ", 6880, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 4, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 2, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 1, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 1]], [[5, 1, 2, 4, 3], [1, 1, 1, 0]]} "Class ", 6881, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 4, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 2, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 1, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 1]], [[5, 1, 2, 4, 3], [0, 0, 0, 1]]} "Class ", 6882, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 4, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 1, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 1]], [[5, 1, 2, 4, 3], [1, 0, 0, 1]]} "Class ", 6883, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 4, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 2, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 1, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[5, 1, 2, 4, 3], [0, 1, 0, 1]]} "Class ", 6884, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 4, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 2, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 1, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 1]], [[5, 1, 2, 4, 3], [1, 1, 0, 1]]} "Class ", 6885, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 4, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 2, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 1, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 4, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 2, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 1, 5], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [ [2, 1, 3, 4, 5], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 4, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 6886, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 4, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 2, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 1, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 4, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 2, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 1, 5], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 6887, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 4, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 2, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 1, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[5, 1, 2, 4, 3], [0, 1, 1, 1]]} "Class ", 6888, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 5, 4, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 5, 4, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 401, 1311, 4375, 14842, 51032, 177443, 622863, 2204225, 7855594, 28169565, 101565203, 367969229, 1338934195, 4891033042] "" "Class ", 6889, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 5, 4, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 5, 4, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}] , [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1221, 3939, 12885, 42636, 142456, 479944, 1628631, 5561411, 19096541, 65896618, 228393724, 794741412, 2775388162] "" "Class ", 6890, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 2, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 4, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 5, 4, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 4, 5, 2, 3], [0, 1, 0, 0]]} "Class ", 6891, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 2, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 4, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 5, 4, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 2, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 4, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 5, 4, 1], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 6892, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 2, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 4, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 5, 4, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 1]], [[1, 4, 5, 2, 3], [0, 0, 1, 0]]} "Class ", 6893, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 2, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 4, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 5, 4, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 2, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 4, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 5, 4, 1], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6894, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 2, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 4, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 5, 4, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 4, 5, 2, 3], [0, 1, 1, 0]]} "Class ", 6895, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 2, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 4, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 5, 4, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 2, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 4, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 5, 4, 1], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0], [0, 1, 0, 1]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 1], [0, 1, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6896, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 2, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 4, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 5, 4, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 2, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 4, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 5, 4, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 401, 1311, 4375, 14842, 51032, 177443, 622863, 2204225, 7855594, 28169565, 101565203, 367969229, 1338934195, 4891033042] "" "Class ", 6897, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 2, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 4, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 5, 4, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 2, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 4, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 5, 4, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}] , [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1221, 3939, 12885, 42636, 142456, 479944, 1628631, 5561411, 19096541, 65896618, 228393724, 794741412, 2775388162] "" "Class ", 6898, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 2, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 4, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 5, 4, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 4, 5, 2, 3], [0, 1, 0, 1]]} "Class ", 6899, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 2, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 4, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 5, 4, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 2, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 4, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 5, 4, 1], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 6900, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 2, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 4, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 5, 4, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 1]], [[1, 4, 5, 2, 3], [0, 0, 1, 1]]} "Class ", 6901, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 2, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 4, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 5, 4, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 2, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 4, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 5, 4, 1], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6902, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 2, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 4, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 5, 4, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 4, 5, 2, 3], [0, 1, 1, 1]]} "Class ", 6903, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 2, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 4, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 5, 4, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 2, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 4, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 5, 4, 1], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2, 5], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0], [0, 1, 0, 1]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 1], [0, 1, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6904, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 5, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 5, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 401, 1311, 4375, 14842, 51032, 177443, 622863, 2204225, 7855594, 28169565, 101565203, 367969229, 1338934195, 4891033042] "" "Class ", 6905, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 5, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 5, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 6906, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 2, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 4, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 5, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 5, 4, 2, 3], [0, 1, 0, 0]]} "Class ", 6907, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 2, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 4, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 5, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 2, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 4, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 5, 1], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [3, 4, 1, 2, 5], {3, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1033, 2986, 8594, 24674, 70757, 202814, 581272, 1666003, 4775323, 13688536, 39240095, 112490042, 322480613] "" "Class ", 6908, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 2, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 4, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 5, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 1]], [[1, 5, 4, 2, 3], [0, 0, 1, 0]]} "Class ", 6909, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 2, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 4, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 5, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 2, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 4, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 5, 1], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [3, 4, 1, 2, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6910, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 2, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 4, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 5, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 5, 4, 2, 3], [0, 1, 1, 0]]} "Class ", 6911, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 2, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 4, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 5, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 2, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 4, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 5, 1], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [3, 4, 1, 2, 5], {3, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1033, 2986, 8594, 24674, 70757, 202814, 581272, 1666003, 4775323, 13688536, 39240095, 112490042, 322480613] "" "Class ", 6912, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 2, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 4, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 5, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 2, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 4, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 5, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 401, 1311, 4375, 14842, 51032, 177443, 622863, 2204225, 7855594, 28169565, 101565203, 367969229, 1338934195, 4891033042] "" "Class ", 6913, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 4, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 5, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 2, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 4, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 5, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 6914, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 2, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 4, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 5, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 5, 4, 2, 3], [0, 1, 0, 1]]} "Class ", 6915, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 2, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 4, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 5, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 2, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 4, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 5, 1], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [3, 4, 1, 2, 5], {3, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1033, 2986, 8594, 24674, 70757, 202814, 581272, 1666003, 4775323, 13688536, 39240095, 112490042, 322480613] "" "Class ", 6916, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 2, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 4, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 5, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 1]], [[1, 5, 4, 2, 3], [0, 0, 1, 1]]} "Class ", 6917, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 2, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 4, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 5, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 2, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 4, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 5, 1], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [3, 4, 1, 2, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6918, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 2, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 4, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 5, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 5, 4, 2, 3], [0, 1, 1, 1]]} "Class ", 6919, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 394, 1273, 4194, 14039, 47614, 163266, 565072, 1971476, 6926313, 24482914, 87009495, 310710172, 1114326403, 4011922558] "" "Class ", 6920, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [ [2, 3, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1220, 3929, 12822, 42309, 140922, 473169, 1599864, 5442561, 18615176, 63975857, 220816906, 765121477, 2660426630] "" "Class ", 6921, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 2, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 4, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 2, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 4, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4, 5], {4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6922, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 2, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 4, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 2, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 4, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [ [2, 3, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6923, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 2, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 4, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 1]], [[5, 1, 4, 2, 3], [0, 0, 1, 0]]} "Class ", 6924, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 2, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 4, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 1]], [[5, 1, 4, 2, 3], [1, 0, 1, 0]]} "Class ", 6925, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 2, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 4, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 2, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 4, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4, 5], {4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6926, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 2, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 4, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 2, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 4, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1, 5], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [ [2, 3, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6927, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 2, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 4, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 2, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 4, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 394, 1273, 4194, 14039, 47614, 163266, 565072, 1971476, 6926313, 24482914, 87009495, 310710172, 1114326403, 4011922558] "" "Class ", 6928, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 2, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 4, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 2, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 4, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [ [2, 3, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1220, 3929, 12822, 42309, 140922, 473169, 1599864, 5442561, 18615176, 63975857, 220816906, 765121477, 2660426630] "" "Class ", 6929, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 2, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 4, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 2, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 4, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4, 5], {4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6930, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 2, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 4, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 2, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 4, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1, 5], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [ [2, 3, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6931, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 2, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 4, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 1]], [[5, 1, 4, 2, 3], [0, 0, 1, 1]]} "Class ", 6932, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 2, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 4, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 1]], [[5, 1, 4, 2, 3], [1, 0, 1, 1]]} "Class ", 6933, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 2, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 4, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 2, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 4, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1, 5], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4, 5], {4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6934, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 5, 4], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 5, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 4, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1267, 4166, 13918, 47109, 161205, 556783, 1938487, 6796031, 23971361, 85009671, 302918609, 1084049439, 3894514424] "" "Class ", 6935, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 5, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 5, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1212, 3885, 12614, 41400, 137132, 457841, 1539150, 5205612, 17700450, 60473476, 207491052, 714668954, 2470156910] "" "Class ", 6936, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 5, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [0, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 5, 4], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [0, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 4, 1, 5], {1, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 6937, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 2, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 4, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 5, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 2, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 4, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 5, 4], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 6938, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 2, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 4, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 5, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 2, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 4, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 5, 4], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1, 5], {1, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {1, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1223, 3961, 13038, 43497, 146756, 499884, 1716674, 5937177, 20661579, 72297570, 254213181, 897770214, 3182999770] "" "Class ", 6939, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 2, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 4, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 5, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 2, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 4, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 5, 4], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, %1], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {3}, %1], [[2, 3, 4, 1], {1, 4}, %1], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} %1 := {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1158, 3615, 11393, 36209, 115940, 373709, 1211740, 3949969, 12937612, 42558745, 140547051, 465799527, 1548766044] "" "Class ", 6940, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 2, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 4, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 5, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 2, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 4, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 5, 4], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1, 5], {1, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6941, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 2, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 4, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 5, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 2, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 4, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 5, 4], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, %1], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {3}, %1], [[2, 3, 4, 1], {4}, %1], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} %1 := {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6942, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 4, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 5, 4], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 4, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 5, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 4, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1267, 4166, 13918, 47109, 161205, 556783, 1938487, 6796031, 23971361, 85009671, 302918609, 1084049439, 3894514424] "" "Class ", 6943, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 2, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 4, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 5, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 2, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 4, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 5, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1212, 3885, 12614, 41400, 137132, 457841, 1539150, 5205612, 17700450, 60473476, 207491052, 714668954, 2470156910] "" "Class ", 6944, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 5, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 5, 4], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 4, 1, 5], {1, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 6945, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 2, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 4, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 5, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 2, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 4, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 5, 4], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 6946, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 2, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 4, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 5, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 2, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 4, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 5, 4], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1, 5], {1, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {1, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1223, 3961, 13038, 43497, 146756, 499884, 1716674, 5937177, 20661579, 72297570, 254213181, 897770214, 3182999770] "" "Class ", 6947, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 2, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 4, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 5, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 2, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 4, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 5, 4], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, %1], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {3}, %1], [[2, 3, 4, 1], {1, 4}, %1], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} %1 := {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1158, 3615, 11393, 36209, 115940, 373709, 1211740, 3949969, 12937612, 42558745, 140547051, 465799527, 1548766044] "" "Class ", 6948, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 4, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 5, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 4, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 5, 4], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1, 5], {1, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6949, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 2, 3], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 4, 3], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 4, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1210, 3867, 12504, 40833, 134482, 446197, 1490068, 5004702, 16895480, 57299652, 195130472, 666990671, 2287644406] "" "Class ", 6950, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 2, 3], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 4, 3], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6951, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 2, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 4, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 2, 3], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 4, 3], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 4, 1, 5], {1, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 6952, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 4, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 4, 3], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6953, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 2, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 4, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 2, 3], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 4, 3], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1, 5], {1, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3604, 11317, 35786, 113863, 364302, 1171436, 3784042, 12274440, 39967252, 130595802, 428110921, 1407595227] "" "Class ", 6954, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 2, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 4, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 2, 3], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 4, 3], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1032, 2973, 8496, 24111, 68017, 190885, 533294, 1484021, 4115186, 11375765, 31358377, 86223943, 236540916] "" "Class ", 6955, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 2, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 4, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 2, 3], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 4, 3], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1, 5], {1, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6956, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 4, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 4, 3], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4, 5], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1032, 2973, 8496, 24111, 68017, 190885, 533294, 1484021, 4115186, 11375765, 31358377, 86223943, 236540916] "" "Class ", 6957, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 4, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 4, 3], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 4, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1210, 3867, 12504, 40833, 134482, 446197, 1490068, 5004702, 16895480, 57299652, 195130472, 666990671, 2287644406] "" "Class ", 6958, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6959, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 4, 1, 5], {1, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 6960, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6961, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 2, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 4, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 2, 3], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 4, 3], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1, 5], {1, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3604, 11317, 35786, 113863, 364302, 1171436, 3784042, 12274440, 39967252, 130595802, 428110921, 1407595227] "" "Class ", 6962, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 2, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 4, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 2, 3], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 4, 3], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1032, 2973, 8496, 24111, 68017, 190885, 533294, 1484021, 4115186, 11375765, 31358377, 86223943, 236540916] "" "Class ", 6963, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 4, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 4, 3], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1, 5], {1, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6964, " is:" {{[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 4, 5, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 5, 4, 3, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 4, 5, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 5, 4, 3, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 1, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}] , [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 127, 408, 1346, 4533, 15518, 53837, 188864, 668802, 2387503, 8582691, 31042653, 112885776, 412482587, 1513699914, 5576428245] "" "Class ", 6965, " is:" {{[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 4, 5, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 5, 4, 3, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 4, 5, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 5, 4, 3, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [4, 1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4158, 13873, 46893, 160247, 552723, 1921756, 6728347, 23701026, 83939765, 298712615, 1067598164, 3830414563] "" "Class ", 6966, " is:" {{[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 4, 5, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 2, 1, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 5, 4, 3, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 3, 4, 5, 2], [0, 1, 0, 0]]} "Class ", 6967, " is:" {{[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 4, 5, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 2, 1, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 5, 4, 3, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 4, 5, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 2, 1, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 5, 4, 3, 1], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 0, 1, 1], [0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1212, 3885, 12614, 41400, 137132, 457841, 1539150, 5205612, 17700450, 60473476, 207491052, 714668954, 2470156910] "" "Class ", 6968, " is:" {{[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 4, 5, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 2, 1, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 5, 4, 3, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 1]], [[1, 3, 4, 5, 2], [0, 0, 1, 0]]} "Class ", 6969, " is:" {{[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 4, 5, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 2, 1, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 5, 4, 3, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 1]], [[1, 3, 4, 5, 2], [1, 0, 1, 0]]} "Class ", 6970, " is:" {{[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 4, 5, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 2, 1, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 5, 4, 3, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 3, 4, 5, 2], [0, 1, 1, 0]]} "Class ", 6971, " is:" {{[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 4, 5, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 2, 1, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 5, 4, 3, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 1]], [[1, 3, 4, 5, 2], [1, 1, 1, 0]]} "Class ", 6972, " is:" {{[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 5, 4, 3, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 1]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]} "Class ", 6973, " is:" {{[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 5, 4, 3, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 1]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]} "Class ", 6974, " is:" {{[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 4, 5, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 2, 1, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 5, 4, 3, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 3, 4, 5, 2], [0, 1, 0, 1]]} "Class ", 6975, " is:" {{[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 4, 5, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 2, 1, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 5, 4, 3, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 1]], [[1, 3, 4, 5, 2], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 4, 5, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 2, 1, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 5, 4, 3, 1], [1, 0, 1, 1]]}}, " the pattern set ", {[[2, 1, 3], [1, 1]], [[1, 3, 4, 5, 2], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6976, " is:" {{[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 4, 5, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 2, 1, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 5, 4, 3, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 1]], [[1, 3, 4, 5, 2], [0, 0, 1, 1]]} "Class ", 6977, " is:" {{[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 4, 5, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 2, 1, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 5, 4, 3, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 1]], [[1, 3, 4, 5, 2], [1, 0, 1, 1]]} "Class ", 6978, " is:" {{[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 4, 5, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 2, 1, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 5, 4, 3, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 3, 4, 5, 2], [0, 1, 1, 1]]} "Class ", 6979, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 5, 4, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 1, 2, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 5, 3, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 5, 4, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 1, 2, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 5, 3, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [[4, 2, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}] , [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 127, 408, 1346, 4533, 15518, 53837, 188864, 668802, 2387503, 8582691, 31042653, 112885776, 412482587, 1513699914, 5576428245] "" "Class ", 6980, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 5, 4, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 1, 2, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 5, 3, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 5, 4, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 1, 2, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 5, 3, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [4, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4158, 13873, 46893, 160247, 552723, 1921756, 6728347, 23701026, 83939765, 298712615, 1067598164, 3830414563] "" "Class ", 6981, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 5, 4, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 1, 2, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 5, 3, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 3, 5, 4, 2], [0, 1, 0, 0]]} "Class ", 6982, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 5, 4, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 1, 2, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 5, 3, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 5, 4, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 1, 2, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 5, 3, 1], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 1, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 6983, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 5, 4, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 1, 2, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 5, 3, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 1]], [[1, 3, 5, 4, 2], [0, 0, 1, 0]]} "Class ", 6984, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 5, 4, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 1, 2, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 5, 3, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 1]], [[1, 3, 5, 4, 2], [1, 0, 1, 0]]} "Class ", 6985, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 5, 4, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 1, 2, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 5, 3, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 3, 5, 4, 2], [0, 1, 1, 0]]} "Class ", 6986, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 5, 4, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 1, 2, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 5, 3, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 5, 4, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 1, 2, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 5, 3, 1], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 1, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6987, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 5, 4, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 1, 2, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 5, 3, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 1]], [[1, 3, 5, 4, 2], [0, 0, 0, 1]]} "Class ", 6988, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 5, 4, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 5, 3, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 1]], [[1, 3, 5, 4, 2], [1, 0, 0, 1]]} "Class ", 6989, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 5, 4, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 1, 2, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 5, 3, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 3, 5, 4, 2], [0, 1, 0, 1]]} "Class ", 6990, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 5, 4, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 1, 2, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 5, 3, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 5, 4, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 1, 2, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 5, 3, 1], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 1, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6991, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 5, 4, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 1, 2, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 5, 3, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 1]], [[1, 3, 5, 4, 2], [0, 0, 1, 1]]} "Class ", 6992, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 5, 4, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 1, 2, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 5, 3, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 1]], [[1, 3, 5, 4, 2], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 5, 4, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 1, 2, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 5, 3, 1], [1, 1, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [1, 1]], [[1, 3, 5, 4, 2], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {2}, {[0, 1, 1, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 6993, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 5, 4, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 1, 2, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 5, 3, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 3, 5, 4, 2], [0, 1, 1, 1]]} "Class ", 6994, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 3, 4, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 3, 2, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 3, 5, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 3, 1, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 3, 4, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 3, 2, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 3, 5, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 2, 3, 1, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}] , [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 127, 408, 1346, 4533, 15518, 53837, 188864, 668802, 2387503, 8582691, 31042653, 112885776, 412482587, 1513699914, 5576428245] "" "Class ", 6995, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 3, 4, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 3, 2, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 3, 5, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 3, 1, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 3, 4, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 3, 2, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 3, 5, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 2, 3, 1, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1220, 3929, 12822, 42309, 140922, 473169, 1599864, 5442561, 18615176, 63975857, 220816906, 765121477, 2660426630] "" "Class ", 6996, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 1, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 3, 4, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 3, 2, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 3, 5, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 3, 1, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 5, 3, 4, 2], [0, 1, 0, 0]]} "Class ", 6997, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 1, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 3, 4, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 3, 2, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 3, 5, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 3, 1, 5], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 1, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 3, 4, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 3, 2, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 3, 5, 1], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 2, 3, 1, 5], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 366, 1106, 3367, 10324, 31865, 98930, 308737, 967904, 3046747, 9625304, 30507667, 96980798, 309121448, 987731324] "" "Class ", 6998, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 1, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 3, 4, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 3, 2, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 3, 5, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 3, 1, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 1]], [[1, 5, 3, 4, 2], [0, 0, 1, 0]]} "Class ", 6999, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 1, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 3, 4, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 3, 2, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 3, 5, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 3, 1, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 1]], [[1, 5, 3, 4, 2], [1, 0, 1, 0]]} "Class ", 7000, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 1, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 3, 4, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 3, 2, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 3, 5, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 3, 1, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 5, 3, 4, 2], [0, 1, 1, 0]]} "Class ", 7001, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 1, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 3, 4, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 3, 2, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 3, 5, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 3, 1, 5], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 1]], [[1, 5, 3, 4, 2], [1, 1, 1, 0]]} "Class ", 7002, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 1, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 3, 4, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 3, 2, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 3, 5, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 3, 1, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 1]], [[1, 5, 3, 4, 2], [0, 0, 0, 1]]} "Class ", 7003, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 1, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 3, 4, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 3, 2, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 3, 5, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 3, 1, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 1]], [[1, 5, 3, 4, 2], [1, 0, 0, 1]]} "Class ", 7004, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 1, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 3, 4, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 3, 2, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 3, 5, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 3, 1, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 5, 3, 4, 2], [0, 1, 0, 1]]} "Class ", 7005, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 1, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 3, 4, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 3, 2, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 3, 5, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 3, 1, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 1]], [[1, 5, 3, 4, 2], [1, 1, 0, 1]]} "Class ", 7006, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 1, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 3, 4, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 3, 2, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 3, 5, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 3, 1, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 1]], [[1, 5, 3, 4, 2], [0, 0, 1, 1]]} "Class ", 7007, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 1, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 3, 4, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 3, 2, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 3, 5, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 3, 1, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 1]], [[1, 5, 3, 4, 2], [1, 0, 1, 1]]} "Class ", 7008, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 1, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 3, 4, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 3, 2, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 3, 5, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 3, 1, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 5, 3, 4, 2], [0, 1, 1, 1]]} "Class ", 7009, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 1, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 3, 4, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 3, 2, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 3, 5, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 3, 1, 5], [1, 1, 1, 1]]} {[[2, 1, 3], [1, 1]], [[1, 5, 3, 4, 2], [1, 1, 1, 1]]} "Class ", 7010, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 3, 4, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 3, 2, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 3, 1, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 3, 5, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 3, 4, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 3, 2, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 3, 1, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 2, 3, 5, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 1, 0, 0]}], [[3, 1, 2, 4, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 3, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 401, 1311, 4376, 14850, 51077, 177660, 623833, 2208378, 7872910, 28240520, 101852500, 369122649, 1343536175, 4909309244] "" "Class ", 7011, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 3, 4, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 3, 2, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 3, 1, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 3, 5, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 3, 4, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 3, 2, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 3, 1, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 2, 3, 5, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4158, 13873, 46893, 160247, 552723, 1921756, 6728347, 23701026, 83939765, 298712615, 1067598164, 3830414563] "" "Class ", 7012, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 5, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 3, 4, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 3, 2, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 3, 1, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 3, 5, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[5, 1, 3, 4, 2], [0, 1, 0, 0]]} "Class ", 7013, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 5, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 3, 4, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 3, 2, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 3, 1, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 3, 5, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 1]], [[5, 1, 3, 4, 2], [1, 1, 0, 0]]} "Class ", 7014, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 5, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 3, 4, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 3, 2, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 3, 1, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 3, 5, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 1]], [[5, 1, 3, 4, 2], [0, 0, 1, 0]]} "Class ", 7015, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 5, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 3, 4, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 3, 2, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 3, 1, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 3, 5, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 1]], [[5, 1, 3, 4, 2], [1, 0, 1, 0]]} "Class ", 7016, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 5, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 3, 4, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 3, 2, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 3, 1, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 3, 5, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[5, 1, 3, 4, 2], [0, 1, 1, 0]]} "Class ", 7017, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 5, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 3, 4, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 3, 2, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 3, 1, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 3, 5, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 1]], [[5, 1, 3, 4, 2], [1, 1, 1, 0]]} "Class ", 7018, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 5, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 3, 4, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 3, 2, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 3, 1, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 3, 5, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 1]], [[5, 1, 3, 4, 2], [0, 0, 0, 1]]} "Class ", 7019, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 5, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 3, 4, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 3, 2, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 3, 1, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 3, 5, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 1]], [[5, 1, 3, 4, 2], [1, 0, 0, 1]]} "Class ", 7020, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 5, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 3, 4, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 3, 2, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 3, 1, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 3, 5, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[5, 1, 3, 4, 2], [0, 1, 0, 1]]} "Class ", 7021, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 5, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 3, 4, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 3, 2, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 3, 1, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 3, 5, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 1]], [[5, 1, 3, 4, 2], [1, 1, 0, 1]]} "Class ", 7022, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 5, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 3, 4, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 3, 2, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 3, 1, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 3, 5, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 1]], [[5, 1, 3, 4, 2], [0, 0, 1, 1]]} "Class ", 7023, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 5, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 3, 4, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 3, 2, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 3, 1, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 3, 5, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 1]], [[5, 1, 3, 4, 2], [1, 0, 1, 1]]} "Class ", 7024, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 5, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 3, 4, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 3, 2, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 3, 1, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 3, 5, 1], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[5, 1, 3, 4, 2], [0, 1, 1, 1]]} "Class ", 7025, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 5, 4, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 5, 4, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}] , [[5, 4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 127, 408, 1346, 4533, 15518, 53837, 188864, 668802, 2387503, 8582691, 31042653, 112885776, 412482587, 1513699914, 5576428245] "" "Class ", 7026, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 5, 4, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 5, 4, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1211, 3875, 12548, 41040, 135370, 449791, 1504057, 5057668, 17092030, 58018150, 197727023, 676290905, 2320721255] "" "Class ", 7027, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 3, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 3, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 5, 4, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 4, 5, 3, 2], [0, 1, 0, 0]]} "Class ", 7028, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 3, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 3, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 5, 4, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 3, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 3, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 5, 4, 1], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {[0, 1, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 7029, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 3, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 3, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 5, 4, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 1]], [[1, 4, 5, 3, 2], [0, 0, 1, 0]]} "Class ", 7030, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 3, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 3, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 5, 4, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 1]], [[1, 4, 5, 3, 2], [1, 0, 1, 0]]} "Class ", 7031, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 3, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 3, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 5, 4, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 4, 5, 3, 2], [0, 1, 1, 0]]} "Class ", 7032, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 3, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 3, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 5, 4, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 3, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 3, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 5, 4, 1], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {[0, 1, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1033, 2986, 8594, 24674, 70757, 202814, 581272, 1666003, 4775323, 13688536, 39240095, 112490042, 322480613] "" "Class ", 7033, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 3, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 3, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 5, 4, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 1]], [[1, 4, 5, 3, 2], [0, 0, 0, 1]]} "Class ", 7034, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 3, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 5, 4, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 1]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]} "Class ", 7035, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 3, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 3, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 5, 4, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 4, 5, 3, 2], [0, 1, 0, 1]]} "Class ", 7036, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 3, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 3, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 5, 4, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 1]], [[1, 4, 5, 3, 2], [1, 1, 0, 1]]} "Class ", 7037, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 3, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 3, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 5, 4, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 1]], [[1, 4, 5, 3, 2], [0, 0, 1, 1]]} "Class ", 7038, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 3, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 3, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 5, 4, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 1]], [[1, 4, 5, 3, 2], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 3, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 3, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 5, 4, 1], [1, 1, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [1, 1]], [[1, 4, 5, 3, 2], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[1, 2, 3, 4], {2}, {[0, 1, 1, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [ [2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1033, 2986, 8594, 24674, 70757, 202814, 581272, 1666003, 4775323, 13688536, 39240095, 112490042, 322480613] "" "Class ", 7039, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 3, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 3, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 5, 4, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 4, 5, 3, 2], [0, 1, 1, 1]]} "Class ", 7040, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [[4, 3, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}] , [[5, 4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {1, 2, 3, 4}, {[0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 127, 408, 1346, 4533, 15518, 53837, 188864, 668802, 2387503, 8582691, 31042653, 112885776, 412482587, 1513699914, 5576428245] "" "Class ", 7041, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1210, 3865, 12482, 40677, 133572, 441468, 1467296, 4900760, 16439370, 55357305, 187050302, 633998079, 2154950454] "" "Class ", 7042, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 3, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 5, 1], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 1, 0, 0]]} "Class ", 7043, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 5, 1], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 5, 1], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3, 5], {4, 5}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 3, 1, 2, 5], {3, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [ [5, 2, 1, 3, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 357, 1053, 3110, 9206, 27319, 81259, 242193, 723110, 2162162, 6473259, 19401540, 58206157, 174772167, 525176245] "" "Class ", 7044, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 3, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 5, 1], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 0, 1, 0]]} "Class ", 7045, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 5, 1], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 5, 1], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1033, 2986, 8594, 24674, 70757, 202814, 581272, 1666003, 4775323, 13688536, 39240095, 112490042, 322480613] "" "Class ", 7046, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 3, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 5, 1], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 1, 1, 0]]} "Class ", 7047, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 5, 1], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 5, 1], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 119, 336, 927, 2527, 6870, 18717, 51155, 140120, 384147, 1053147, 2886182, 7906953, 21657679, 59318944, 162475127] "" "Class ", 7048, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 5, 1], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]} "Class ", 7049, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 5, 1], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]} "Class ", 7050, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 3, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 5, 1], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 1, 0, 1]]} "Class ", 7051, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 5, 1], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 5, 1], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1]}], [[4, 2, 1, 3, 5], {4, 5}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 3, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 120, 346, 984, 2775, 7797, 21889, 61474, 172757, 485727, 1366035, 3842119, 10806399, 30393424, 85480456, 240406851] "" "Class ", 7052, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 3, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 5, 1], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 0, 1, 1]]} "Class ", 7053, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 5, 1], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 5, 1], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1033, 2986, 8594, 24674, 70757, 202814, 581272, 1666003, 4775323, 13688536, 39240095, 112490042, 322480613] "" "Class ", 7054, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 3, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 5, 1], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[1, 5, 4, 3, 2], [0, 1, 1, 1]]} "Class ", 7055, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 5, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 5, 1], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 119, 336, 927, 2527, 6870, 18717, 51155, 140120, 384147, 1053147, 2886182, 7906953, 21657679, 59318944, 162475127] "" "Class ", 7056, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [ [3, 2, 1, 4, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 401, 1311, 4376, 14850, 51077, 177660, 623833, 2208378, 7872910, 28240520, 101852500, 369122649, 1343536175, 4909309244] "" "Class ", 7057, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4158, 13873, 46893, 160247, 552723, 1921756, 6728347, 23701026, 83939765, 298712615, 1067598164, 3830414563] "" "Class ", 7058, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 3, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 3, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 3, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 3, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [[3, 2, 1, 4, 5], {4}, %1], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 3, 5], {4}, %1], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 2, 5], {3}, %1], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 3, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0, 0]}]} %1 := {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 7059, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 3, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 3, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [ [4, 2, 1, 3, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [ [4, 3, 1, 2, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [ [5, 2, 1, 3, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 7060, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 3, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 3, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 1]], [[5, 1, 4, 3, 2], [0, 0, 1, 0]]} "Class ", 7061, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 3, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 3, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 1]], [[5, 1, 4, 3, 2], [1, 0, 1, 0]]} "Class ", 7062, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 3, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 3, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 3, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 3, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [ [3, 2, 1, 4, 5], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 356, 1044, 3057, 8948, 26192, 76674, 224465, 657137, 1923817, 5632105, 16488346, 48270655, 141315320, 413709331] "" "Class ", 7063, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 3, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 3, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 3, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 3, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1, 5], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 356, 1044, 3057, 8948, 26192, 76674, 224465, 657137, 1923817, 5632105, 16488346, 48270655, 141315320, 413709331] "" "Class ", 7064, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 3, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 3, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 1]], [[5, 1, 4, 3, 2], [0, 0, 0, 1]]} "Class ", 7065, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 3, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 3, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 1]], [[5, 1, 4, 3, 2], [1, 0, 0, 1]]} "Class ", 7066, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 3, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 3, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 3, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 3, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [ [3, 2, 1, 4, 5], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 3, 5], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 3, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7067, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 3, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 3, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 3, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [ [4, 2, 1, 3, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [ [5, 2, 1, 3, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7068, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 3, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 3, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 1]], [[5, 1, 4, 3, 2], [0, 0, 1, 1]]} "Class ", 7069, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 3, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 3, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 1]], [[5, 1, 4, 3, 2], [1, 0, 1, 1]]} "Class ", 7070, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 3, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 3, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 3, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 3, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [ [3, 2, 1, 4, 5], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 356, 1044, 3057, 8948, 26192, 76674, 224465, 657137, 1923817, 5632105, 16488346, 48270655, 141315320, 413709331] "" "Class ", 7071, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 5, 4], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 5, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 401, 1310, 4369, 14814, 50913, 176958, 620929, 2196606, 7825793, 28053502, 101114369, 366220798, 1332159745, 4864798206] "" "Class ", 7072, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 5, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 5, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4158, 13873, 46893, 160247, 552723, 1921756, 6728347, 23701026, 83939765, 298712615, 1067598164, 3830414563] "" "Class ", 7073, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 3, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 5, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [0, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 3, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 5, 4], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [0, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 7074, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 3, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 3, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 5, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 3, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 3, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 5, 4], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 7075, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 3, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 5, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 3, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 5, 4], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1222, 3951, 12974, 43163, 145198, 493089, 1688266, 5821647, 20200416, 70480443, 247119160, 870262599, 3076876534] "" "Class ", 7076, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 3, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 3, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 5, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 3, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 3, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 5, 4], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1158, 3615, 11393, 36209, 115940, 373709, 1211740, 3949969, 12937612, 42558745, 140547051, 465799527, 1548766044] "" "Class ", 7077, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 3, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 5, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 3, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 5, 4], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7078, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 3, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 3, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 5, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 3, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 3, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 5, 4], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7079, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 3, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 5, 4], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 0, 0, 1]]} "Class ", 7080, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 3, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 3, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 5, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 1]], [[4, 5, 1, 3, 2], [1, 0, 0, 1]]} "Class ", 7081, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 3, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 5, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 1, 0, 1]]} "Class ", 7082, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 3, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 3, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 5, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 1]], [[4, 5, 1, 3, 2], [1, 1, 0, 1]]} "Class ", 7083, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 3, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 5, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 3, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 5, 4], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1222, 3951, 12974, 43163, 145198, 493089, 1688266, 5821647, 20200416, 70480443, 247119160, 870262599, 3076876534] "" "Class ", 7084, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 3, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 3, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 5, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 3, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 3, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 5, 4], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1158, 3615, 11393, 36209, 115940, 373709, 1211740, 3949969, 12937612, 42558745, 140547051, 465799527, 1548766044] "" "Class ", 7085, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 3, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 5, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 3, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 3, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 5, 4], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7086, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 3, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}] , [[4, 3, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1267, 4166, 13918, 47109, 161205, 556783, 1938487, 6796031, 23971361, 85009671, 302918609, 1084049439, 3894514424] "" "Class ", 7087, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 3, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 377, 1179, 3754, 12139, 39769, 131737, 440521, 1485092, 5042054, 17224693, 59166043, 204224955, 708009769, 2464197596] "" "Class ", 7088, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 3, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 3, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 1, 2], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 7089, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 3, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 3, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 3, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 3, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 366, 1105, 3356, 10251, 31483, 97186, 301431, 939004, 2936896, 9219531, 29040111, 91757034, 290754383, 923769926] "" "Class ", 7090, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 3, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 3, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 1, 2], {1, 2, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1158, 3615, 11393, 36209, 115940, 373709, 1211740, 3949969, 12937612, 42558745, 140547051, 465799527, 1548766044] "" "Class ", 7091, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 3, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 3, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 3, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 3, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1032, 2973, 8496, 24111, 68017, 190885, 533294, 1484021, 4115186, 11375765, 31358377, 86223943, 236540916] "" "Class ", 7092, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 3, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 3, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 1, 2], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7093, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 3, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 3, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4, 5], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1032, 2973, 8496, 24111, 68017, 190885, 533294, 1484021, 4115186, 11375765, 31358377, 86223943, 236540916] "" "Class ", 7094, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 3, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 0, 0, 0]]} {[[2, 1, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 0, 0, 1]]} "Class ", 7095, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 3, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 0, 0, 1]]} {[[2, 1, 3], [1, 1]], [[5, 4, 1, 3, 2], [1, 0, 0, 1]]} "Class ", 7096, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 3, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 1, 0, 1]]} "Class ", 7097, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 3, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 1]], [[5, 4, 1, 3, 2], [1, 1, 0, 1]]} "Class ", 7098, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 3, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 3, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 1, 2], {1, 2, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1158, 3615, 11393, 36209, 115940, 373709, 1211740, 3949969, 12937612, 42558745, 140547051, 465799527, 1548766044] "" "Class ", 7099, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 3, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 3, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 3, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 3, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1032, 2973, 8496, 24111, 68017, 190885, 533294, 1484021, 4115186, 11375765, 31358377, 86223943, 236540916] "" "Class ", 7100, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 3, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 3, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 3, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 1, 2], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7101, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 5, 4, 3], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 5, 4, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 401, 1311, 4376, 14850, 51077, 177660, 623833, 2208378, 7872910, 28240520, 101852500, 369122649, 1343536175, 4909309244] "" "Class ", 7102, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 5, 4, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 5, 4, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1267, 4167, 13928, 47175, 161563, 558527, 1946444, 6830829, 24119213, 85625143, 305442436, 1094281935, 3935638646] "" "Class ", 7103, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 1, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 5, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 5, 4, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[3, 4, 5, 1, 2], [0, 1, 0, 0]]} "Class ", 7104, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 1, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 5, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 5, 4, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 1, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 5, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 5, 4, 3], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [0, 2, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1212, 3885, 12614, 41400, 137132, 457841, 1539150, 5205612, 17700450, 60473476, 207491052, 714668954, 2470156910] "" "Class ", 7105, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 7106, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 5, 4, 3], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7107, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 1, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 5, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 5, 4, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 1, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 5, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 5, 4, 3], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 7108, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 1, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 5, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 5, 4, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 1, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 5, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 5, 4, 3], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0], [0, 2, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0], [0, 0, 2, 0, 0], [0, 1, 1, 0, 0], [0, 2, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7109, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 5, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 5, 4, 3], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 1, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 5, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 5, 4, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 401, 1311, 4376, 14850, 51077, 177660, 623833, 2208378, 7872910, 28240520, 101852500, 369122649, 1343536175, 4909309244] "" "Class ", 7110, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 1, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 5, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 5, 4, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 1, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 5, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 5, 4, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1267, 4167, 13928, 47175, 161563, 558527, 1946444, 6830829, 24119213, 85625143, 305442436, 1094281935, 3935638646] "" "Class ", 7111, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 1, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 5, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 5, 4, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[3, 4, 5, 1, 2], [0, 1, 0, 1]]} "Class ", 7112, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 1, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 5, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 5, 4, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 1, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 5, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 5, 4, 3], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [0, 2, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1212, 3885, 12614, 41400, 137132, 457841, 1539150, 5205612, 17700450, 60473476, 207491052, 714668954, 2470156910] "" "Class ", 7113, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 1, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 5, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 5, 4, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 1, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 5, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 5, 4, 3], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 7114, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 1, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 5, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 5, 4, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 1, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 5, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 5, 4, 3], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7115, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 1, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 5, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 5, 4, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 1, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 5, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 5, 4, 3], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 7116, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 5, 3], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 5, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1, 5], {1, 2, 3}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 401, 1311, 4376, 14850, 51077, 177660, 623833, 2208378, 7872910, 28240520, 101852500, 369122649, 1343536175, 4909309244] "" "Class ", 7117, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 5, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 5, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1211, 3875, 12548, 41040, 135370, 449791, 1504057, 5057668, 17092030, 58018150, 197727023, 676290905, 2320721255] "" "Class ", 7118, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 5, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 5, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 1, 0, 0]]} "Class ", 7119, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 1, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 5, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 5, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 1, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 5, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 5, 3], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [ [3, 4, 1, 2, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1158, 3615, 11393, 36209, 115940, 373709, 1211740, 3949969, 12937612, 42558745, 140547051, 465799527, 1548766044] "" "Class ", 7120, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 5, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 5, 3], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1, 5], {1, 2, 3}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 7121, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 5, 3], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7122, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 5, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 5, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 1, 1, 0]]} "Class ", 7123, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 1, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 5, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 5, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 1, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 5, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 5, 3], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7124, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 5, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 5, 3], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 5, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 5, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1, 5], {1, 2, 3}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 401, 1311, 4376, 14850, 51077, 177660, 623833, 2208378, 7872910, 28240520, 101852500, 369122649, 1343536175, 4909309244] "" "Class ", 7125, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 1, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 5, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 5, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 1, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 5, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 5, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1211, 3875, 12548, 41040, 135370, 449791, 1504057, 5057668, 17092030, 58018150, 197727023, 676290905, 2320721255] "" "Class ", 7126, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 5, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 5, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 1, 0, 1]]} "Class ", 7127, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 1, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 5, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 5, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 1, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 5, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 5, 3], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [ [3, 4, 1, 2, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1158, 3615, 11393, 36209, 115940, 373709, 1211740, 3949969, 12937612, 42558745, 140547051, 465799527, 1548766044] "" "Class ", 7128, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 5, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 5, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 5, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 5, 3], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1, 5], {1, 2, 3}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 7129, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 1, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 5, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 5, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 1, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 5, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 5, 3], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7130, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 5, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 5, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[3, 5, 4, 1, 2], [0, 1, 1, 1]]} "Class ", 7131, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 394, 1273, 4194, 14039, 47614, 163266, 565072, 1971476, 6926313, 24482914, 87009495, 310710172, 1114326403, 4011922558] "" "Class ", 7132, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 377, 1180, 3763, 12189, 39994, 132647, 444000, 1497995, 5089109, 17394637, 59776318, 206409201, 715813258, 2492053352] "" "Class ", 7133, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 1, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 5, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[5, 3, 4, 1, 2], [0, 1, 0, 0]]} "Class ", 7134, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 1, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 5, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 1]], [[5, 3, 4, 1, 2], [1, 1, 0, 0]]} "Class ", 7135, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3, 5], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7136, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 354, 1021, 2901, 8130, 22513, 61713, 167746, 452789, 1215197, 3246050, 8637641, 22912633, 60624546, 160075117] "" "Class ", 7137, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 1, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 5, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 1, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 5, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3, 5], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7138, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 1, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 5, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 1, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 5, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3, 5], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 354, 1021, 2901, 8130, 22513, 61713, 167746, 452789, 1215197, 3246050, 8637641, 22912633, 60624546, 160075117] "" "Class ", 7139, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 5, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 5, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 394, 1273, 4194, 14039, 47614, 163266, 565072, 1971476, 6926313, 24482914, 87009495, 310710172, 1114326403, 4011922558] "" "Class ", 7140, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 5, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 5, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 377, 1180, 3763, 12189, 39994, 132647, 444000, 1497995, 5089109, 17394637, 59776318, 206409201, 715813258, 2492053352] "" "Class ", 7141, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 1, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 5, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[5, 3, 4, 1, 2], [0, 1, 0, 1]]} "Class ", 7142, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 1, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 5, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [1, 0, 1, 1]]} {[[2, 1, 3], [1, 1]], [[5, 3, 4, 1, 2], [1, 1, 0, 1]]} "Class ", 7143, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 5, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 5, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3, 5], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7144, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 5, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 5, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3, 5], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 354, 1021, 2901, 8130, 22513, 61713, 167746, 452789, 1215197, 3246050, 8637641, 22912633, 60624546, 160075117] "" "Class ", 7145, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 1, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 5, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 1, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 5, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3, 5], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7146, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 5, 4], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 5, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1, 5], {1, 2, 3}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4159, 13883, 46959, 160608, 554500, 1929947, 6764488, 23855708, 84587419, 301380544, 1078453368, 3874161462] "" "Class ", 7147, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 5, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 5, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1211, 3875, 12548, 41040, 135370, 449791, 1504057, 5057668, 17092030, 58018150, 197727023, 676290905, 2320721255] "" "Class ", 7148, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 5, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 5, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 5, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 5, 4], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1, 5], {3, 5}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {4}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 354, 1021, 2901, 8130, 22513, 61713, 167746, 452789, 1215197, 3246050, 8637641, 22912633, 60624546, 160075117] "" "Class ", 7149, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 1, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 5, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 5, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 1, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 5, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 5, 4], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 354, 1021, 2901, 8130, 22513, 61713, 167746, 452789, 1215197, 3246050, 8637641, 22912633, 60624546, 160075117] "" "Class ", 7150, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 5, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 5, 4], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1, 5], {1, 2, 3}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 7151, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7152, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 5, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 5, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 5, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 5, 4], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1, 5], {3, 5}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {4}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 354, 1021, 2901, 8130, 22513, 61713, 167746, 452789, 1215197, 3246050, 8637641, 22912633, 60624546, 160075117] "" "Class ", 7153, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 1, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 5, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 5, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 1, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 5, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 5, 4], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 354, 1021, 2901, 8130, 22513, 61713, 167746, 452789, 1215197, 3246050, 8637641, 22912633, 60624546, 160075117] "" "Class ", 7154, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 5, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 5, 4], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 5, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 5, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1, 5], {1, 2, 3}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4159, 13883, 46959, 160608, 554500, 1929947, 6764488, 23855708, 84587419, 301380544, 1078453368, 3874161462] "" "Class ", 7155, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 1, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 5, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 5, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 1, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 5, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 5, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1211, 3875, 12548, 41040, 135370, 449791, 1504057, 5057668, 17092030, 58018150, 197727023, 676290905, 2320721255] "" "Class ", 7156, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 5, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 5, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 5, 4], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1, 5], {3, 5}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {4}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 354, 1021, 2901, 8130, 22513, 61713, 167746, 452789, 1215197, 3246050, 8637641, 22912633, 60624546, 160075117] "" "Class ", 7157, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 1, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 5, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 5, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 1, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 5, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 5, 4], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 354, 1021, 2901, 8130, 22513, 61713, 167746, 452789, 1215197, 3246050, 8637641, 22912633, 60624546, 160075117] "" "Class ", 7158, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 5, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 5, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 5, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 5, 4], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1, 5], {1, 2, 3}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 7159, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 1, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 5, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 5, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 1, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 5, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 5, 4], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7160, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 5, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 5, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 1, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 5, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 5, 4], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1, 5], {3, 5}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {4}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 354, 1021, 2901, 8130, 22513, 61713, 167746, 452789, 1215197, 3246050, 8637641, 22912633, 60624546, 160075117] "" "Class ", 7161, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 1, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 5, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 5, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 1, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 5, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 5, 4], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 3, 1, 2], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 354, 1021, 2901, 8130, 22513, 61713, 167746, 452789, 1215197, 3246050, 8637641, 22912633, 60624546, 160075117] "" "Class ", 7162, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 5, 4], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1, 5], {1, 2, 3}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1210, 3865, 12482, 40677, 133572, 441468, 1467296, 4900760, 16439370, 55357305, 187050302, 633998079, 2154950454] "" "Class ", 7163, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 5, 4], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 356, 1042, 3037, 8827, 25618, 74315, 215632, 626120, 1819845, 5295578, 15428589, 45006923, 131450682, 384376649] "" "Class ", 7164, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 5, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 5, 4], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1, 5], {3, 5}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {4}, {[0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 354, 1021, 2901, 8130, 22513, 61713, 167746, 452789, 1215197, 3246050, 8637641, 22912633, 60624546, 160075117] "" "Class ", 7165, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 5, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 5, 4], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 119, 334, 902, 2351, 5945, 14660, 35408, 84061, 196715, 454778, 1040522, 2359451, 5308589, 11862208, 26345684] "" "Class ", 7166, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 5, 4], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1, 5], {1, 2, 3}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 7167, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 120, 345, 972, 2691, 7348, 19855, 53230, 141871, 376466, 995705, 2627018, 6918101, 18192804, 47791365, 125443416] "" "Class ", 7168, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 5, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 5, 4], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1, 5], {3, 5}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {4}, {[0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 354, 1021, 2901, 8130, 22513, 61713, 167746, 452789, 1215197, 3246050, 8637641, 22912633, 60624546, 160075117] "" "Class ", 7169, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 5, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 5, 4], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4, 5], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 119, 334, 902, 2351, 5945, 14660, 35408, 84061, 196715, 454778, 1040522, 2359451, 5308589, 11862208, 26345684] "" "Class ", 7170, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1, 5], {1, 2, 3}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1210, 3865, 12482, 40677, 133572, 441468, 1467296, 4900760, 16439370, 55357305, 187050302, 633998079, 2154950454] "" "Class ", 7171, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 356, 1042, 3037, 8827, 25618, 74315, 215632, 626120, 1819845, 5295578, 15428589, 45006923, 131450682, 384376649] "" "Class ", 7172, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1, 5], {3, 5}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {4}, {[0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 354, 1021, 2901, 8130, 22513, 61713, 167746, 452789, 1215197, 3246050, 8637641, 22912633, 60624546, 160075117] "" "Class ", 7173, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 5, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 5, 4], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 119, 334, 902, 2351, 5945, 14660, 35408, 84061, 196715, 454778, 1040522, 2359451, 5308589, 11862208, 26345684] "" "Class ", 7174, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 5, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 5, 4], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1, 5], {1, 2, 3}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 7175, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 5, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 5, 4], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 120, 345, 972, 2691, 7348, 19855, 53230, 141871, 376466, 995705, 2627018, 6918101, 18192804, 47791365, 125443416] "" "Class ", 7176, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 5, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 5, 4], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1, 5], {3, 5}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {4}, {[0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 354, 1021, 2901, 8130, 22513, 61713, 167746, 452789, 1215197, 3246050, 8637641, 22912633, 60624546, 160075117] "" "Class ", 7177, " is:" {{[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 1, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 127, 408, 1346, 4533, 15518, 53837, 188864, 668802, 2387503, 8582691, 31042653, 112885776, 412482587, 1513699914, 5576428245] "" "Class ", 7178, " is:" {{[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 4, 5, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 4, 5, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 5, 4, 3, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [4, 1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 401, 1310, 4369, 14814, 50913, 176958, 620929, 2196606, 7825793, 28053502, 101114369, 366220798, 1332159745, 4864798206] "" "Class ", 7179, " is:" {{[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 4, 5, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 5, 4, 3, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[2, 3, 4, 5, 1], [0, 1, 0, 0]]} "Class ", 7180, " is:" {{[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 4, 5, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 5, 4, 3, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 4, 5, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 5, 4, 3, 2], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 0, 2, 0], [0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1265, 4150, 13828, 46674, 159262, 548498, 1904179, 6656720, 23413351, 82796431, 294203641, 1049919648, 3761410985] "" "Class ", 7181, " is:" {{[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 4, 5, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 5, 4, 3, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 1]], [[2, 3, 4, 5, 1], [0, 0, 1, 0]]} "Class ", 7182, " is:" {{[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 4, 5, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 5, 4, 3, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 1]], [[2, 3, 4, 5, 1], [1, 0, 1, 0]]} "Class ", 7183, " is:" {{[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 4, 5, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 5, 4, 3, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[2, 3, 4, 5, 1], [0, 1, 1, 0]]} "Class ", 7184, " is:" {{[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 4, 5, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 5, 4, 3, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 1]], [[2, 3, 4, 5, 1], [1, 1, 1, 0]]} "Class ", 7185, " is:" {{[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 4, 5, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1210, 3865, 12482, 40677, 133572, 441468, 1467296, 4900760, 16439370, 55357305, 187050302, 633998079, 2154950454] "" "Class ", 7186, " is:" {{[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 4, 5, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 4, 5, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [4, 1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 7187, " is:" {{[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 4, 5, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 4, 5, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {2}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 7188, " is:" {{[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 4, 5, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 4, 5, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 5, 4, 3, 2], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 0, 2, 0], [0, 1, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7189, " is:" {{[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 4, 5, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 4, 5, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1210, 3865, 12482, 40677, 133572, 441468, 1467296, 4900760, 16439370, 55357305, 187050302, 633998079, 2154950454] "" "Class ", 7190, " is:" {{[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 4, 5, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 4, 5, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 5, 4, 3, 2], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [4, 1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 7191, " is:" {{[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 4, 5, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 4, 5, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {2}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 7192, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 5, 4, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 5, 3, 2], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 5, 4, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 5, 3, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [ [4, 2, 1, 3, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 127, 408, 1346, 4533, 15518, 53837, 188864, 668802, 2387503, 8582691, 31042653, 112885776, 412482587, 1513699914, 5576428245] "" "Class ", 7193, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 5, 4, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 5, 3, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 5, 4, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 5, 3, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [4, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 401, 1310, 4369, 14814, 50913, 176958, 620929, 2196606, 7825793, 28053502, 101114369, 366220798, 1332159745, 4864798206] "" "Class ", 7194, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 5, 4, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 5, 3, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[2, 3, 5, 4, 1], [0, 1, 0, 0]]} "Class ", 7195, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 5, 4, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 5, 3, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 5, 4, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 5, 3, 2], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 2, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1211, 3875, 12548, 41040, 135370, 449791, 1504057, 5057668, 17092030, 58018150, 197727023, 676290905, 2320721255] "" "Class ", 7196, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 5, 4, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 5, 3, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 1]], [[2, 3, 5, 4, 1], [0, 0, 1, 0]]} "Class ", 7197, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 5, 4, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 5, 3, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 1]], [[2, 3, 5, 4, 1], [1, 0, 1, 0]]} "Class ", 7198, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 5, 4, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 5, 3, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[2, 3, 5, 4, 1], [0, 1, 1, 0]]} "Class ", 7199, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 5, 4, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 5, 3, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 5, 4, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 5, 3, 2], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 2, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 7200, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 5, 4, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 5, 3, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 5, 4, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 5, 3, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}], [ [4, 2, 1, 3, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1211, 3875, 12548, 41040, 135370, 449791, 1504057, 5057668, 17092030, 58018150, 197727023, 676290905, 2320721255] "" "Class ", 7201, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 5, 4, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 5, 4, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 5, 3, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [4, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 7202, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 5, 4, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 5, 3, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 5, 4, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 5, 3, 2], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}], [ [4, 2, 1, 3, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 7203, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 5, 4, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 5, 3, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 5, 4, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 5, 3, 2], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {[0, 0, 2, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7204, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 5, 4, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 5, 3, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 1]], [[2, 3, 5, 4, 1], [0, 0, 1, 1]]} "Class ", 7205, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 5, 4, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 5, 3, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 1]], [[2, 3, 5, 4, 1], [1, 0, 1, 1]]} "Class ", 7206, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 5, 4, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 5, 3, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 5, 4, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 5, 3, 2], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}], [ [4, 2, 1, 3, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 7207, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 3, 4, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 5, 2], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 3, 4, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 5, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 127, 408, 1346, 4533, 15518, 53837, 188864, 668802, 2387503, 8582691, 31042653, 112885776, 412482587, 1513699914, 5576428245] "" "Class ", 7208, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 3, 4, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 5, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 3, 4, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 5, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4158, 13873, 46893, 160247, 552723, 1921756, 6728347, 23701026, 83939765, 298712615, 1067598164, 3830414563] "" "Class ", 7209, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 3, 4, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 5, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[2, 5, 3, 4, 1], [0, 1, 0, 0]]} "Class ", 7210, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 3, 4, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 5, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 3, 4, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 5, 2], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1222, 3951, 12974, 43163, 145198, 493089, 1688266, 5821647, 20200416, 70480443, 247119160, 870262599, 3076876534] "" "Class ", 7211, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 3, 4, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 5, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 1]], [[2, 5, 3, 4, 1], [0, 0, 1, 0]]} "Class ", 7212, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 3, 4, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 5, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 1]], [[2, 5, 3, 4, 1], [1, 0, 1, 0]]} "Class ", 7213, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 3, 4, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 5, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[2, 5, 3, 4, 1], [0, 1, 1, 0]]} "Class ", 7214, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 3, 4, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 5, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 1]], [[2, 5, 3, 4, 1], [1, 1, 1, 0]]} "Class ", 7215, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 3, 4, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 5, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 3, 4, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 5, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {2, 3, 4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1220, 3929, 12822, 42309, 140922, 473169, 1599864, 5442561, 18615176, 63975857, 220816906, 765121477, 2660426630] "" "Class ", 7216, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 3, 4, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 5, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 3, 4, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 5, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7217, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 3, 4, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 5, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[2, 5, 3, 4, 1], [0, 1, 0, 1]]} "Class ", 7218, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 3, 4, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 5, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 3, 4, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 5, 2], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7219, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 3, 4, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 5, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 3, 4, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 5, 2], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {2, 3, 4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1220, 3929, 12822, 42309, 140922, 473169, 1599864, 5442561, 18615176, 63975857, 220816906, 765121477, 2660426630] "" "Class ", 7220, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 3, 4, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 5, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 3, 4, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 5, 2], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7221, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 3, 4, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 5, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[2, 5, 3, 4, 1], [0, 1, 1, 1]]} "Class ", 7222, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 3, 4, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 3, 4, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 1, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 401, 1311, 4375, 14842, 51032, 177443, 622863, 2204225, 7855594, 28169565, 101565203, 367969229, 1338934195, 4891033042] "" "Class ", 7223, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 3, 4, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 3, 4, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [4, 1, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 386, 1232, 4016, 13321, 44824, 152637, 525001, 1821233, 6364492, 22384264, 79171069, 281421171, 1004802960, 3601987092] "" "Class ", 7224, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 3, 4, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[5, 2, 3, 4, 1], [0, 1, 0, 0]]} "Class ", 7225, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 3, 4, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 1]], [[5, 2, 3, 4, 1], [1, 1, 0, 0]]} "Class ", 7226, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 3, 4, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 1]], [[5, 2, 3, 4, 1], [0, 0, 1, 0]]} "Class ", 7227, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 3, 4, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 1]], [[5, 2, 3, 4, 1], [1, 0, 1, 0]]} "Class ", 7228, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 3, 4, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[5, 2, 3, 4, 1], [0, 1, 1, 0]]} "Class ", 7229, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 3, 4, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [0, 1, 1, 1]]} {[[2, 1, 3], [1, 1]], [[5, 2, 3, 4, 1], [1, 1, 1, 0]]} "Class ", 7230, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 3, 4, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 3, 4, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 7231, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 3, 4, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 3, 4, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [4, 1, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7232, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 3, 4, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 3, 4, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [ [5, 1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7233, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 3, 4, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 3, 4, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2, 5], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [4, 1, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1032, 2973, 8496, 24111, 68017, 190885, 533294, 1484021, 4115186, 11375765, 31358377, 86223943, 236540916] "" "Class ", 7234, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 3, 4, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 3, 4, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2, 5], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 7235, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 3, 4, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 3, 4, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2, 5], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [4, 1, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7236, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 3, 4, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 3, 4, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2, 5], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [ [5, 1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7237, " is:" {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 3, 4, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 3, 4, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2, 5], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 2, 3, 4, 1], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [4, 1, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1032, 2973, 8496, 24111, 68017, 190885, 533294, 1484021, 4115186, 11375765, 31358377, 86223943, 236540916] "" "Class ", 7238, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 4, 5, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 2, 1, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 5, 4, 2], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 4, 5, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 2, 1, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 5, 4, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [ [4, 3, 1, 2, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 127, 408, 1346, 4533, 15518, 53837, 188864, 668802, 2387503, 8582691, 31042653, 112885776, 412482587, 1513699914, 5576428245] "" "Class ", 7239, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 4, 5, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 2, 1, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 5, 4, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 4, 5, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 2, 1, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 5, 4, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1265, 4149, 13818, 46608, 158898, 546685, 1895715, 6618905, 23249607, 82103555, 291322471, 1038099516, 3713430835] "" "Class ", 7240, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 4, 5, 3, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 2, 1, 3, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 5, 4, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[2, 4, 5, 3, 1], [0, 1, 0, 0]]} "Class ", 7241, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 4, 5, 3, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 2, 1, 3, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 5, 4, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 4, 5, 3, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 2, 1, 3, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 5, 4, 2], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {[0, 1, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1220, 3929, 12822, 42309, 140922, 473169, 1599864, 5442561, 18615176, 63975857, 220816906, 765121477, 2660426630] "" "Class ", 7242, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 4, 5, 3, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 2, 1, 3, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 5, 4, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 1]], [[2, 4, 5, 3, 1], [0, 0, 1, 0]]} "Class ", 7243, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 4, 5, 3, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 2, 1, 3, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 5, 4, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 1]], [[2, 4, 5, 3, 1], [1, 0, 1, 0]]} "Class ", 7244, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 4, 5, 3, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 2, 1, 3, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 5, 4, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[2, 4, 5, 3, 1], [0, 1, 1, 0]]} "Class ", 7245, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 4, 5, 3, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 2, 1, 3, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 5, 4, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 4, 5, 3, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 2, 1, 3, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 5, 4, 2], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {[0, 1, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7246, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 4, 5, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 2, 1, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 5, 4, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 4, 5, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 2, 1, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 5, 4, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}], [ [4, 3, 1, 2, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {2, 3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4158, 13873, 46893, 160247, 552723, 1921756, 6728347, 23701026, 83939765, 298712615, 1067598164, 3830414563] "" "Class ", 7247, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 4, 5, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 2, 1, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 5, 4, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 4, 5, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 2, 1, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 5, 4, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 7248, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 4, 5, 3, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 2, 1, 3, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 5, 4, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[2, 4, 5, 3, 1], [0, 1, 0, 1]]} "Class ", 7249, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 4, 5, 3, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 2, 1, 3, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 5, 4, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 4, 5, 3, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 2, 1, 3, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 5, 4, 2], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {[0, 1, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7250, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 4, 5, 3, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 2, 1, 3, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 5, 4, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 1]], [[2, 4, 5, 3, 1], [0, 0, 1, 1]]} "Class ", 7251, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 4, 5, 3, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 2, 1, 3, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 5, 4, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 1]], [[2, 4, 5, 3, 1], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 4, 5, 3, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 2, 1, 3, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 5, 4, 2], [1, 1, 0, 1]]}}, " the pattern set ", {[[2, 1, 3], [1, 1]], [[2, 4, 5, 3, 1], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1}, {[1, 1, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7252, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 4, 5, 3, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 2, 1, 3, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 5, 4, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[2, 4, 5, 3, 1], [0, 1, 1, 1]]} "Class ", 7253, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 4, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 5, 2], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 4, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 5, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {1, 2, 3, 4}, {[0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 127, 408, 1346, 4533, 15518, 53837, 188864, 668802, 2387503, 8582691, 31042653, 112885776, 412482587, 1513699914, 5576428245] "" "Class ", 7254, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 4, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 4, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 5, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1221, 3939, 12886, 42648, 142544, 480459, 1631287, 5574073, 19153815, 66146259, 229452587, 799140681, 2793373937] "" "Class ", 7255, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 4, 3, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 5, 2], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[2, 5, 4, 3, 1], [0, 1, 0, 0]]} "Class ", 7256, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 4, 3, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 5, 2], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 4, 3, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 5, 2], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 1, 0]}], [[4, 3, 1, 2, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {3, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 367, 1116, 3429, 10636, 33271, 104866, 332763, 1062330, 3409877, 10998602, 35632815, 115903574, 378372911, 1239314162] "" "Class ", 7257, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 4, 3, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 5, 2], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 1]], [[2, 5, 4, 3, 1], [0, 0, 1, 0]]} "Class ", 7258, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 4, 3, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 5, 2], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 4, 3, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 5, 2], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7259, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 4, 3, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 5, 2], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[2, 5, 4, 3, 1], [0, 1, 1, 0]]} "Class ", 7260, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 4, 3, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 5, 2], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 4, 3, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 5, 2], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 356, 1044, 3057, 8948, 26192, 76674, 224465, 657137, 1923817, 5632105, 16488346, 48270655, 141315320, 413709331] "" "Class ", 7261, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 4, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 5, 2], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 4, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 5, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {2, 3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {2, 3, 4}, {[0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4158, 13873, 46893, 160247, 552723, 1921756, 6728347, 23701026, 83939765, 298712615, 1067598164, 3830414563] "" "Class ", 7262, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 4, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 4, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 5, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 7263, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 4, 3, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 5, 2], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[2, 5, 4, 3, 1], [0, 1, 0, 1]]} "Class ", 7264, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 4, 3, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 5, 2], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 4, 3, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 5, 2], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 356, 1044, 3057, 8948, 26192, 76674, 224465, 657137, 1923817, 5632105, 16488346, 48270655, 141315320, 413709331] "" "Class ", 7265, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 4, 3, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 5, 2], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 1]], [[2, 5, 4, 3, 1], [0, 0, 1, 1]]} "Class ", 7266, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 4, 3, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 5, 2], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 4, 3, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 5, 2], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7267, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 4, 3, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 5, 2], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[2, 5, 4, 3, 1], [0, 1, 1, 1]]} "Class ", 7268, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 4, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 4, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [ [4, 2, 1, 3, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 401, 1311, 4375, 14842, 51032, 177443, 622863, 2204225, 7855594, 28169565, 101565203, 367969229, 1338934195, 4891033042] "" "Class ", 7269, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 386, 1232, 4016, 13321, 44824, 152637, 525001, 1821233, 6364492, 22384264, 79171069, 281421171, 1004802960, 3601987092] "" "Class ", 7270, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 4, 3, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[5, 2, 4, 3, 1], [0, 1, 0, 0]]} "Class ", 7271, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [0, 0, 1, 1]]} {[[2, 1, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 1, 0, 0]]} "Class ", 7272, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 4, 3, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [0, 1, 0, 0]]} {[[2, 1, 3], [1, 1]], [[5, 2, 4, 3, 1], [0, 0, 1, 0]]} "Class ", 7273, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [0, 1, 0, 1]]} {[[2, 1, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 0, 1, 0]]} "Class ", 7274, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 4, 3, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 4, 3, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2, 5], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}], [ [4, 2, 1, 3, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 3, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7275, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2, 5], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1032, 2973, 8496, 24111, 68017, 190885, 533294, 1484021, 4115186, 11375765, 31358377, 86223943, 236540916] "" "Class ", 7276, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 4, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 4, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}], [ [4, 2, 1, 3, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 3, 4], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1221, 3939, 12885, 42636, 142456, 479944, 1628631, 5561411, 19096541, 65896618, 228393724, 794741412, 2775388162] "" "Class ", 7277, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 3, 1, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 366, 1105, 3356, 10251, 31483, 97186, 301431, 939004, 2936896, 9219531, 29040111, 91757034, 290754383, 923769926] "" "Class ", 7278, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 4, 3, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 4, 3, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}], [ [4, 2, 1, 3, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 3, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7279, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2, 5], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1032, 2973, 8496, 24111, 68017, 190885, 533294, 1484021, 4115186, 11375765, 31358377, 86223943, 236540916] "" "Class ", 7280, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 4, 3, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [1, 1, 0, 0]]} {[[2, 1, 3], [1, 1]], [[5, 2, 4, 3, 1], [0, 0, 1, 1]]} "Class ", 7281, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [1, 1, 0, 1]]} {[[2, 1, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 0, 1, 1]]} "Class ", 7282, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 4, 3, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 4, 3, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2, 5], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}], [ [4, 2, 1, 3, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 3, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7283, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 2, 4, 3, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2, 5], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 2, 4, 1], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1032, 2973, 8496, 24111, 68017, 190885, 533294, 1484021, 4115186, 11375765, 31358377, 86223943, 236540916] "" "Class ", 7284, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 5, 4], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 5, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 402, 1317, 4403, 14963, 51537, 179503, 631144, 2237199, 7986056, 28683449, 103583004, 375874395, 1369853869, 5011826841] "" "Class ", 7285, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 2, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 5, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 2, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 5, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 394, 1273, 4193, 14029, 47551, 162935, 563487, 1964305, 6895072, 24350348, 86457606, 308445117, 1105131089, 3974909434] "" "Class ", 7286, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 5, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [0, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 5, 4], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [0, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {4, 5}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1095, 3294, 9943, 30136, 91754, 280693, 862816, 2664635, 8266165, 25751860, 80543830, 252844693, 796443768] "" "Class ", 7287, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 2, 3, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 5, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 2, 3, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 5, 4], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1095, 3294, 9943, 30136, 91754, 280693, 862816, 2664635, 8266165, 25751860, 80543830, 252844693, 796443768] "" "Class ", 7288, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 5, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 5, 4], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {2, 3, 4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1221, 3939, 12885, 42636, 142456, 479944, 1628631, 5561411, 19096541, 65896618, 228393724, 794741412, 2775388162] "" "Class ", 7289, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 2, 3, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 5, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 2, 3, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 5, 4], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 7290, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 5, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 5, 4], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {4, 5}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 354, 1021, 2901, 8130, 22513, 61713, 167746, 452789, 1215197, 3246050, 8637641, 22912633, 60624546, 160075117] "" "Class ", 7291, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 2, 3, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 5, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 2, 3, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 5, 4], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 354, 1021, 2901, 8130, 22513, 61713, 167746, 452789, 1215197, 3246050, 8637641, 22912633, 60624546, 160075117] "" "Class ", 7292, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 5, 4], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 5, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {2, 3, 4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1221, 3939, 12885, 42636, 142456, 479944, 1628631, 5561411, 19096541, 65896618, 228393724, 794741412, 2775388162] "" "Class ", 7293, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 2, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 5, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 2, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 5, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 7294, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 5, 4], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {4, 5}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 354, 1021, 2901, 8130, 22513, 61713, 167746, 452789, 1215197, 3246050, 8637641, 22912633, 60624546, 160075117] "" "Class ", 7295, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 5, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 2, 3, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 5, 4], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 354, 1021, 2901, 8130, 22513, 61713, 167746, 452789, 1215197, 3246050, 8637641, 22912633, 60624546, 160075117] "" "Class ", 7296, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 5, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 5, 4], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {2, 3, 4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1221, 3939, 12885, 42636, 142456, 479944, 1628631, 5561411, 19096541, 65896618, 228393724, 794741412, 2775388162] "" "Class ", 7297, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 2, 3, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 5, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 2, 3, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 5, 4], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 7298, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 5, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 2, 3, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 5, 4], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {4, 5}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 354, 1021, 2901, 8130, 22513, 61713, 167746, 452789, 1215197, 3246050, 8637641, 22912633, 60624546, 160075117] "" "Class ", 7299, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 2, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 2, 3, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4157, 13863, 46827, 159886, 550943, 1913526, 6691891, 23544320, 83280751, 295986327, 1056461081, 3785365874] "" "Class ", 7300, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 2, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 2, 3, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3}, {[0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 369, 1138, 3577, 11434, 37077, 121694, 403537, 1349874, 4549601, 15434722, 52665073, 180616786, 622250597, 2152493550] "" "Class ", 7301, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4, 5], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {4, 5}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {4}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1095, 3294, 9943, 30136, 91754, 280693, 862816, 2664635, 8266165, 25751860, 80543830, 252844693, 796443768] "" "Class ", 7302, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4, 5], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3}, {[0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 120, 347, 996, 2860, 8265, 24115, 71114, 211903, 637468, 1934027, 5911590, 18188070, 56281929, 175050672, 546926233] "" "Class ", 7303, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 2, 3, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 2, 3, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4, 5], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 7304, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 2, 3, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 2, 3, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4, 5], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3}, {[0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 120, 345, 972, 2691, 7348, 19855, 53230, 141871, 376466, 995705, 2627018, 6918101, 18192804, 47791365, 125443416] "" "Class ", 7305, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 2, 3, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 2, 3, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4, 5], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {4, 5}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {4}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 354, 1021, 2901, 8130, 22513, 61713, 167746, 452789, 1215197, 3246050, 8637641, 22912633, 60624546, 160075117] "" "Class ", 7306, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 2, 3, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 2, 3, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4, 5], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3}, {[0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 119, 334, 902, 2351, 5945, 14660, 35408, 84061, 196715, 454778, 1040522, 2359451, 5308589, 11862208, 26345684] "" "Class ", 7307, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 2, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 2, 3, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 7308, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3}, {[0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 120, 345, 972, 2691, 7348, 19855, 53230, 141871, 376466, 995705, 2627018, 6918101, 18192804, 47791365, 125443416] "" "Class ", 7309, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {4, 5}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {4}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 354, 1021, 2901, 8130, 22513, 61713, 167746, 452789, 1215197, 3246050, 8637641, 22912633, 60624546, 160075117] "" "Class ", 7310, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4, 5], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3}, {[0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 119, 334, 902, 2351, 5945, 14660, 35408, 84061, 196715, 454778, 1040522, 2359451, 5308589, 11862208, 26345684] "" "Class ", 7311, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 2, 3, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 2, 3, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4, 5], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 7312, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 2, 3, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 2, 3, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4, 5], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3}, {[0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 120, 345, 972, 2691, 7348, 19855, 53230, 141871, 376466, 995705, 2627018, 6918101, 18192804, 47791365, 125443416] "" "Class ", 7313, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 2, 3, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 2, 3, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4, 5], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {4, 5}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {4}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 354, 1021, 2901, 8130, 22513, 61713, 167746, 452789, 1215197, 3246050, 8637641, 22912633, 60624546, 160075117] "" "Class ", 7314, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 5, 4, 3], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 5, 4, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [ [4, 3, 1, 2, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 401, 1310, 4368, 14806, 50868, 176738, 619932, 2192288, 7807625, 27978530, 100809146, 364990184, 1327233335, 4845181810] "" "Class ", 7315, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 5, 4, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 5, 4, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1265, 4149, 13818, 46608, 158898, 546685, 1895715, 6618905, 23249607, 82103555, 291322471, 1038099516, 3713430835] "" "Class ", 7316, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 2, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 5, 4, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[3, 4, 5, 2, 1], [0, 1, 0, 0]]} "Class ", 7317, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 2, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 5, 4, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 2, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 5, 4, 3], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {[0, 2, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1211, 3875, 12548, 41040, 135370, 449791, 1504057, 5057668, 17092030, 58018150, 197727023, 676290905, 2320721255] "" "Class ", 7318, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 5, 4, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 5, 4, 3], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [ [4, 3, 1, 2, 5], {1, 3, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 3, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {3, 4}, {[0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7319, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 5, 4, 3], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1032, 2973, 8496, 24111, 68017, 190885, 533294, 1484021, 4115186, 11375765, 31358377, 86223943, 236540916] "" "Class ", 7320, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 2, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 5, 4, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 2, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 5, 4, 3], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [ [4, 3, 1, 2, 5], {1, 3, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 3, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {3, 4}, {[0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7321, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 2, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 5, 4, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 2, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 5, 4, 3], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {[0, 2, 0, 0]}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {[0, 0, 2, 0, 0], [0, 1, 1, 0, 0], [0, 2, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1032, 2973, 8496, 24111, 68017, 190885, 533294, 1484021, 4115186, 11375765, 31358377, 86223943, 236540916] "" "Class ", 7322, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 5, 4, 3], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 5, 4, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}], [ [4, 3, 1, 2, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4158, 13873, 46893, 160247, 552723, 1921756, 6728347, 23701026, 83939765, 298712615, 1067598164, 3830414563] "" "Class ", 7323, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 5, 4, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1212, 3885, 12614, 41400, 137132, 457841, 1539150, 5205612, 17700450, 60473476, 207491052, 714668954, 2470156910] "" "Class ", 7324, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 2, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 5, 4, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[3, 4, 5, 2, 1], [0, 1, 0, 1]]} "Class ", 7325, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 2, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 5, 4, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 2, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 5, 4, 3], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {[0, 2, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394] "" "Class ", 7326, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 2, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 5, 4, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 2, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 5, 4, 3], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [ [4, 3, 1, 2, 5], {1, 3, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 3, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {3, 4}, {[0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7327, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 2, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 2, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 5, 4, 3], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1032, 2973, 8496, 24111, 68017, 190885, 533294, 1484021, 4115186, 11375765, 31358377, 86223943, 236540916] "" "Class ", 7328, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 2, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 5, 4, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 2, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 5, 4, 3], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [ [4, 3, 1, 2, 5], {1, 3, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 3, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {3, 4}, {[0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7329, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 5, 3], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 5, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {1, 2, 3, 4}, {[0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 126, 401, 1310, 4368, 14806, 50868, 176738, 619932, 2192288, 7807625, 27978530, 100809146, 364990184, 1327233335, 4845181810] "" "Class ", 7330, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 5, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1221, 3939, 12886, 42648, 142544, 480459, 1631287, 5574073, 19153815, 66146259, 229452587, 799140681, 2793373937] "" "Class ", 7331, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 5, 3], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [0, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 1, 0, 0]]} "Class ", 7332, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 2, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 5, 3], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 2, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 5, 3], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 1, 0, 0]}], [[4, 3, 1, 2, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 376, 1168, 3678, 11716, 37688, 122261, 399533, 1314023, 4346226, 14447993, 48245641, 161758744, 544337525, 1837867537] "" "Class ", 7333, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 5, 3], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 5, 3], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 2, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 2, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {3, 4}, {[0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 366, 1105, 3356, 10251, 31483, 97186, 301431, 939004, 2936896, 9219531, 29040111, 91757034, 290754383, 923769926] "" "Class ", 7334, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 5, 3], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1032, 2973, 8496, 24111, 68017, 190885, 533294, 1484021, 4115186, 11375765, 31358377, 86223943, 236540916] "" "Class ", 7335, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 5, 3], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [0, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 1, 1, 0]]} "Class ", 7336, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 2, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 5, 3], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 2, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 5, 3], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1032, 2973, 8496, 24111, 68017, 190885, 533294, 1484021, 4115186, 11375765, 31358377, 86223943, 236540916] "" "Class ", 7337, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 5, 3], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 5, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {2, 3, 4}, {[0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4158, 13873, 46893, 160247, 552723, 1921756, 6728347, 23701026, 83939765, 298712615, 1067598164, 3830414563] "" "Class ", 7338, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 5, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 7339, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 5, 3], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [1, 0, 1, 0]]} {[[2, 1, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 1, 0, 1]]} "Class ", 7340, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 2, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 5, 3], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 2, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 5, 3], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7341, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 5, 3], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 5, 3], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 2, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 2, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {3, 4}, {[0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 366, 1105, 3356, 10251, 31483, 97186, 301431, 939004, 2936896, 9219531, 29040111, 91757034, 290754383, 923769926] "" "Class ", 7342, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 2, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 2, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 5, 3], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1032, 2973, 8496, 24111, 68017, 190885, 533294, 1484021, 4115186, 11375765, 31358377, 86223943, 236540916] "" "Class ", 7343, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 5, 3], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [1, 1, 1, 0]]} {[[2, 1, 3], [1, 1]], [[3, 5, 4, 2, 1], [0, 1, 1, 1]]} "Class ", 7344, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}], [ [4, 3, 1, 2, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1266, 4157, 13863, 46827, 159886, 550943, 1913526, 6691891, 23544320, 83280751, 295986327, 1056461081, 3785365874] "" "Class ", 7345, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 368, 1126, 3496, 11008, 35111, 113283, 369200, 1213879, 4021786, 13414608, 45009415, 151810413, 514428560, 1750508062] "" "Class ", 7346, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [0, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3, 5], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [0, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [ [4, 3, 1, 2, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1158, 3615, 11393, 36209, 115940, 373709, 1211740, 3949969, 12937612, 42558745, 140547051, 465799527, 1548766044] "" "Class ", 7347, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3, 5], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 357, 1054, 3121, 9286, 27793, 83722, 253851, 774588, 2377735, 7339580, 22771805, 70982103, 222199591, 698254036] "" "Class ", 7348, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3, 5], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [ [4, 3, 1, 2, 5], {1, 3, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 3, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1032, 2973, 8496, 24111, 68017, 190885, 533294, 1484021, 4115186, 11375765, 31358377, 86223943, 236540916] "" "Class ", 7349, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3, 5], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 119, 334, 902, 2351, 5945, 14660, 35408, 84061, 196715, 454778, 1040522, 2359451, 5308589, 11862208, 26345684] "" "Class ", 7350, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3, 5], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [ [4, 3, 1, 2, 5], {1, 3, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 3, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1032, 2973, 8496, 24111, 68017, 190885, 533294, 1484021, 4115186, 11375765, 31358377, 86223943, 236540916] "" "Class ", 7351, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3, 5], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 119, 334, 902, 2351, 5945, 14660, 35408, 84061, 196715, 454778, 1040522, 2359451, 5308589, 11862208, 26345684] "" "Class ", 7352, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}], [ [4, 3, 1, 2, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {2, 3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1220, 3929, 12822, 42309, 140922, 473169, 1599864, 5442561, 18615176, 63975857, 220816906, 765121477, 2660426630] "" "Class ", 7353, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 357, 1055, 3132, 9358, 28161, 85351, 260431, 799583, 2468725, 7660981, 23882778, 74762599, 234917916, 740685121] "" "Class ", 7354, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [ [4, 3, 1, 2, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7355, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3, 5], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 120, 345, 972, 2691, 7348, 19855, 53230, 141871, 376466, 995705, 2627018, 6918101, 18192804, 47791365, 125443416] "" "Class ", 7356, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3, 5], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [ [4, 3, 1, 2, 5], {1, 3, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 3, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1032, 2973, 8496, 24111, 68017, 190885, 533294, 1484021, 4115186, 11375765, 31358377, 86223943, 236540916] "" "Class ", 7357, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3, 5], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 119, 334, 902, 2351, 5945, 14660, 35408, 84061, 196715, 454778, 1040522, 2359451, 5308589, 11862208, 26345684] "" "Class ", 7358, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 2, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3, 5], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [ [4, 3, 1, 2, 5], {1, 3, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 1, 2, 4], {1, 3, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1032, 2973, 8496, 24111, 68017, 190885, 533294, 1484021, 4115186, 11375765, 31358377, 86223943, 236540916] "" "Class ", 7359, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 5, 4], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 5, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1265, 4148, 13808, 46542, 158534, 544869, 1887212, 6580775, 23083823, 81399079, 288380766, 1025982051, 3664054185] "" "Class ", 7360, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 5, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 385, 1221, 3939, 12886, 42648, 142544, 480459, 1631287, 5574073, 19153815, 66146259, 229452587, 799140681, 2793373937] "" "Class ", 7361, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 5, 4], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 5, 4], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {1, 5}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1031, 2964, 8447, 23907, 67316, 188872, 528751, 1478571, 4133498, 11560364, 32361315, 90707911, 254649934] "" "Class ", 7362, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 5, 4], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 5, 4], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1031, 2964, 8447, 23907, 67316, 188872, 528751, 1478571, 4133498, 11560364, 32361315, 90707911, 254649934] "" "Class ", 7363, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 5, 4], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 5, 4], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 2, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 2, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 366, 1105, 3356, 10251, 31483, 97186, 301431, 939004, 2936896, 9219531, 29040111, 91757034, 290754383, 923769926] "" "Class ", 7364, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 5, 4], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1032, 2973, 8496, 24111, 68017, 190885, 533294, 1484021, 4115186, 11375765, 31358377, 86223943, 236540916] "" "Class ", 7365, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 5, 4], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 5, 4], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {1, 5}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 119, 334, 902, 2351, 5945, 14660, 35408, 84061, 196715, 454778, 1040522, 2359451, 5308589, 11862208, 26345684] "" "Class ", 7366, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 5, 4], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 5, 4], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 119, 334, 902, 2351, 5945, 14660, 35408, 84061, 196715, 454778, 1040522, 2359451, 5308589, 11862208, 26345684] "" "Class ", 7367, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 5, 4], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 5, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {2, 3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1211, 3875, 12548, 41040, 135370, 449791, 1504057, 5057668, 17092030, 58018150, 197727023, 676290905, 2320721255] "" "Class ", 7368, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 5, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140, 3703963, 11921353, 38467475, 124409280, 403183707, 1309058762] "" "Class ", 7369, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 5, 4], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {1, 5}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 120, 344, 960, 2608, 6912, 17920, 45568, 113920, 280576, 681984, 1638400, 3895296, 9175040, 21430272, 49676288] "" "Class ", 7370, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 5, 4], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 5, 4], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 120, 344, 960, 2608, 6912, 17920, 45568, 113920, 280576, 681984, 1638400, 3895296, 9175040, 21430272, 49676288] "" "Class ", 7371, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 5, 4], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 5, 4], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 2, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 2, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 366, 1105, 3356, 10251, 31483, 97186, 301431, 939004, 2936896, 9219531, 29040111, 91757034, 290754383, 923769926] "" "Class ", 7372, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 5, 4], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 2, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 5, 4], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1032, 2973, 8496, 24111, 68017, 190885, 533294, 1484021, 4115186, 11375765, 31358377, 86223943, 236540916] "" "Class ", 7373, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 5, 4], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 2, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 5, 4], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {1, 5}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 119, 334, 902, 2351, 5945, 14660, 35408, 84061, 196715, 454778, 1040522, 2359451, 5308589, 11862208, 26345684] "" "Class ", 7374, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {1, 2, 3, 4}, {[0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 125, 393, 1265, 4147, 13798, 46476, 158170, 543050, 1878670, 6542330, 22915999, 80682987, 285378270, 1013564805, 3613262795] "" "Class ", 7375, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 361, 1094, 3368, 10519, 33269, 106362, 343193, 1116188, 3655336, 12043017, 39889065, 132747674, 443648571, 1488358040] "" "Class ", 7376, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {1, 5}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {4}, {[0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1031, 2964, 8447, 23907, 67316, 188872, 528751, 1478571, 4133498, 11560364, 32361315, 90707911, 254649934] "" "Class ", 7377, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 118, 328, 886, 2353, 6207, 16379, 43415, 115825, 311204, 841999, 2292938, 6280965, 17296253, 47855169, 132967225] "" "Class ", 7378, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 2, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 2, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {3, 4}, {[0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7379, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 118, 324, 845, 2106, 5059, 11807, 26948, 60455, 133820, 293110, 636615, 1373216, 2945265, 6286633, 13363382] "" "Class ", 7380, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {1, 5}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {4}, {[0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 119, 334, 902, 2351, 5945, 14660, 35408, 84061, 196715, 454778, 1040522, 2359451, 5308589, 11862208, 26345684] "" "Class ", 7381, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 0]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 116, 302, 715, 1549, 3106, 5831, 10352, 17525, 28484, 44696, 68021, 100777, 145810, 206569, 287186] "" "Class ", 7382, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {2, 3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {2, 3, 4}, {[0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 124, 384, 1210, 3865, 12482, 40677, 133572, 441468, 1467296, 4900760, 16439370, 55357305, 187050302, 633998079, 2154950454] "" "Class ", 7383, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 120, 348, 1002, 2876, 8253, 23717, 68306, 197200, 570671, 1655112, 4810025, 14004288, 40840413, 119279153, 348837048] "" "Class ", 7384, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {1, 5}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {4}, {[0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 120, 344, 960, 2608, 6912, 17920, 45568, 113920, 280576, 681984, 1638400, 3895296, 9175040, 21430272, 49676288] "" "Class ", 7385, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 117, 314, 789, 1872, 4242, 9279, 19768, 41307, 85123, 173704, 352063, 710266, 1428488, 2867125, 5747018] "" "Class ", 7386, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 2, 1], [0, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4, 5], [0, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 2, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 2, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {3, 4}, {[0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7387, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 2, 1], [1, 0, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4, 5], [1, 0, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 118, 324, 845, 2106, 5059, 11807, 26948, 60455, 133820, 293110, 636615, 1373216, 2945265, 6286633, 13363382] "" "Class ", 7388, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 0]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 2, 1], [0, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4, 5], [0, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {}, {}], [ [4, 3, 2, 1, 5], {1, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 2, 1, 4], {1, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 2, 1, 3], {1, 5}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 1, 2], {4}, {[0, 1, 0, 0, 0, 0]}], [[5, 4, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 119, 334, 902, 2351, 5945, 14660, 35408, 84061, 196715, 454778, 1040522, 2359451, 5308589, 11862208, 26345684] "" "Class ", 7389, " is:" {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4, 5], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 4, 3, 2, 1], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 116, 302, 715, 1549, 3106, 5831, 10352, 17525, 28484, 44696, 68021, 100777, 145810, 206569, 287186] "" "Class ", 7390, " is:" {{%2, [[2, 5, 1, 4, 3], [1, 1, 1, 1]]}, {%2, [[3, 1, 5, 4, 2], [1, 1, 1, 1]]}, {%2, [[3, 2, 5, 1, 4], [1, 1, 1, 1]]}, {%2, [[4, 2, 1, 5, 3], [1, 1, 1, 1]]}, {%1, [[2, 4, 5, 1, 3], [1, 1, 1, 1]]}, {%1, [[3, 4, 1, 5, 2], [1, 1, 1, 1]]}, {%1, [[3, 5, 1, 2, 4], [1, 1, 1, 1]]}, {%1, [[4, 1, 5, 2, 3], [1, 1, 1, 1]]}} %1 := [[3, 2, 1], [1, 1]] %2 := [[1, 2, 3], [1, 1]] {[[1, 2, 3], [1, 1]], [[2, 5, 1, 4, 3], [1, 1, 1, 1]]} "For the class ", {{%1, [[2, 5, 1, 4, 3], [1, 1, 1, 1]]}, {%1, [[3, 1, 5, 4, 2], [1, 1, 1, 1]]}, {%1, [[3, 2, 5, 1, 4], [1, 1, 1, 1]]}, {%1, [[4, 2, 1, 5, 3], [1, 1, 1, 1]]}, {%2, [[2, 4, 5, 1, 3], [1, 1, 1, 1]]}, {%2, [[3, 4, 1, 5, 2], [1, 1, 1, 1]]}, {%2, [[3, 5, 1, 2, 4], [1, 1, 1, 1]]}, {%2, [[4, 1, 5, 2, 3], [1, 1, 1, 1]]}}, " the pattern set ", {%1, [[2, 5, 1, 4, 3], [1, 1, 1, 1]]}, " has scheme:" %1 := [[1, 2, 3], [1, 1]] %2 := [[3, 2, 1], [1, 1]] {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 2, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7391, " is:" {{%2, [[2, 5, 4, 1, 3], [1, 1, 1, 1]]}, {%2, [[3, 5, 2, 1, 4], [1, 1, 1, 1]]}, {%2, [[4, 1, 5, 3, 2], [1, 1, 1, 1]]}, {%2, [[4, 3, 1, 5, 2], [1, 1, 1, 1]]}, {%1, [[2, 3, 5, 1, 4], [1, 1, 1, 1]]}, {%1, [[2, 5, 1, 3, 4], [1, 1, 1, 1]]}, {%1, [[3, 1, 4, 5, 2], [1, 1, 1, 1]]}, {%1, [[4, 1, 2, 5, 3], [1, 1, 1, 1]]}} %1 := [[3, 2, 1], [1, 1]] %2 := [[1, 2, 3], [1, 1]] {[[1, 2, 3], [1, 1]], [[2, 5, 4, 1, 3], [1, 1, 1, 1]]} "For the class ", {{%1, [[2, 5, 4, 1, 3], [1, 1, 1, 1]]}, {%1, [[3, 5, 2, 1, 4], [1, 1, 1, 1]]}, {%1, [[4, 1, 5, 3, 2], [1, 1, 1, 1]]}, {%1, [[4, 3, 1, 5, 2], [1, 1, 1, 1]]}, {%2, [[2, 3, 5, 1, 4], [1, 1, 1, 1]]}, {%2, [[2, 5, 1, 3, 4], [1, 1, 1, 1]]}, {%2, [[3, 1, 4, 5, 2], [1, 1, 1, 1]]}, {%2, [[4, 1, 2, 5, 3], [1, 1, 1, 1]]}}, " the pattern set ", {%1, [[2, 5, 4, 1, 3], [1, 1, 1, 1]]}, " has scheme:" %1 := [[1, 2, 3], [1, 1]] %2 := [[3, 2, 1], [1, 1]] {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, %1], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, %1], [[3, 4, 1, 2], {1, 2}, %1], [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [3, 5, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} %1 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 364, 1083, 3208, 9462, 27812, 81545, 238696, 698005, 2040025, 5960779, 17415475, 50882771, 148670706, 434413073] "" "Class ", 7392, " is:" {{%2, [[2, 5, 4, 3, 1], [1, 1, 1, 1]]}, {%2, [[4, 3, 2, 5, 1], [1, 1, 1, 1]]}, {%2, [[5, 1, 4, 3, 2], [1, 1, 1, 1]]}, {%2, [[5, 3, 2, 1, 4], [1, 1, 1, 1]]}, {%1, [[1, 3, 4, 5, 2], [1, 1, 1, 1]]}, {%1, [[1, 5, 2, 3, 4], [1, 1, 1, 1]]}, {%1, [[2, 3, 4, 1, 5], [1, 1, 1, 1]]}, {%1, [[4, 1, 2, 3, 5], [1, 1, 1, 1]]}} %1 := [[3, 2, 1], [1, 1]] %2 := [[1, 2, 3], [1, 1]] {[[1, 2, 3], [1, 1]], [[2, 5, 4, 3, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 1]], [[4, 3, 2, 5, 1], [1, 1, 1, 1]]} "For the class ", {{%1, [[2, 5, 4, 3, 1], [1, 1, 1, 1]]}, {%1, [[4, 3, 2, 5, 1], [1, 1, 1, 1]]}, {%1, [[5, 1, 4, 3, 2], [1, 1, 1, 1]]}, {%1, [[5, 3, 2, 1, 4], [1, 1, 1, 1]]}, {%2, [[1, 3, 4, 5, 2], [1, 1, 1, 1]]}, {%2, [[1, 5, 2, 3, 4], [1, 1, 1, 1]]}, {%2, [[2, 3, 4, 1, 5], [1, 1, 1, 1]]}, {%2, [[4, 1, 2, 3, 5], [1, 1, 1, 1]]}}, " the pattern set ", {%1, [[4, 3, 2, 5, 1], [1, 1, 1, 1]]}, " has scheme:" %1 := [[1, 2, 3], [1, 1]] %2 := [[3, 2, 1], [1, 1]] {[[], {}, {}], [[1], {}, {}], [[1, 2], {2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 4}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 3, 1, 2], {1, 2, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 3, 2, 1], {1}, {[0, 1, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 119, 336, 924, 2492, 6636, 17536, 46137, 121095, 317434, 831571, 2177734, 5702191, 14929519, 39087182, 102332996] "" "Class ", 7393, " is:" {{%2, [[3, 5, 2, 4, 1], [1, 1, 1, 1]]}, {%2, [[4, 2, 5, 3, 1], [1, 1, 1, 1]]}, {%2, [[5, 2, 4, 1, 3], [1, 1, 1, 1]]}, {%2, [[5, 3, 1, 4, 2], [1, 1, 1, 1]]}, {%1, [[1, 3, 5, 2, 4], [1, 1, 1, 1]]}, {%1, [[1, 4, 2, 5, 3], [1, 1, 1, 1]]}, {%1, [[2, 4, 1, 3, 5], [1, 1, 1, 1]]}, {%1, [[3, 1, 4, 2, 5], [1, 1, 1, 1]]}} %1 := [[3, 2, 1], [1, 1]] %2 := [[1, 2, 3], [1, 1]] {[[1, 2, 3], [1, 1]], [[3, 5, 2, 4, 1], [1, 1, 1, 1]]} "For the class ", {{%1, [[3, 5, 2, 4, 1], [1, 1, 1, 1]]}, {%1, [[4, 2, 5, 3, 1], [1, 1, 1, 1]]}, {%1, [[5, 2, 4, 1, 3], [1, 1, 1, 1]]}, {%1, [[5, 3, 1, 4, 2], [1, 1, 1, 1]]}, {%2, [[1, 3, 5, 2, 4], [1, 1, 1, 1]]}, {%2, [[1, 4, 2, 5, 3], [1, 1, 1, 1]]}, {%2, [[2, 4, 1, 3, 5], [1, 1, 1, 1]]}, {%2, [[3, 1, 4, 2, 5], [1, 1, 1, 1]]}}, " the pattern set ", {%1, [[3, 5, 2, 4, 1], [1, 1, 1, 1]]}, " has scheme:" %1 := [[1, 2, 3], [1, 1]] %2 := [[3, 2, 1], [1, 1]] {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1], [0, 1, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 120, 345, 972, 2691, 7348, 19855, 53230, 141871, 376466, 995705, 2627018, 6918101, 18192804, 47791365, 125443416] "" "Class ", 7394, " is:" {{%2, [[3, 5, 4, 1, 2], [1, 1, 1, 1]]}, {%2, [[4, 3, 5, 1, 2], [1, 1, 1, 1]]}, {%2, [[4, 5, 1, 3, 2], [1, 1, 1, 1]]}, {%2, [[4, 5, 2, 1, 3], [1, 1, 1, 1]]}, {%1, [[2, 1, 4, 5, 3], [1, 1, 1, 1]]}, {%1, [[2, 1, 5, 3, 4], [1, 1, 1, 1]]}, {%1, [[2, 3, 1, 5, 4], [1, 1, 1, 1]]}, {%1, [[3, 1, 2, 5, 4], [1, 1, 1, 1]]}} %1 := [[3, 2, 1], [1, 1]] %2 := [[1, 2, 3], [1, 1]] {[[1, 2, 3], [1, 1]], [[3, 5, 4, 1, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 1]], [[4, 3, 5, 1, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 1]], [[4, 5, 1, 3, 2], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 1]], [[4, 5, 2, 1, 3], [1, 1, 1, 1]]} "Class ", 7395, " is:" {{%2, [[3, 5, 4, 2, 1], [1, 1, 1, 1]]}, {%2, [[4, 3, 5, 2, 1], [1, 1, 1, 1]]}, {%2, [[5, 4, 1, 3, 2], [1, 1, 1, 1]]}, {%2, [[5, 4, 2, 1, 3], [1, 1, 1, 1]]}, {%1, [[1, 2, 4, 5, 3], [1, 1, 1, 1]]}, {%1, [[1, 2, 5, 3, 4], [1, 1, 1, 1]]}, {%1, [[2, 3, 1, 4, 5], [1, 1, 1, 1]]}, {%1, [[3, 1, 2, 4, 5], [1, 1, 1, 1]]}} %1 := [[3, 2, 1], [1, 1]] %2 := [[1, 2, 3], [1, 1]] {[[1, 2, 3], [1, 1]], [[3, 5, 4, 2, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 1]], [[4, 3, 5, 2, 1], [1, 1, 1, 1]]} {[[1, 2, 3], [1, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 1]]} "For the class ", {{%1, [[3, 5, 4, 2, 1], [1, 1, 1, 1]]}, {%1, [[4, 3, 5, 2, 1], [1, 1, 1, 1]]}, {%1, [[5, 4, 1, 3, 2], [1, 1, 1, 1]]}, {%1, [[5, 4, 2, 1, 3], [1, 1, 1, 1]]}, {%2, [[1, 2, 4, 5, 3], [1, 1, 1, 1]]}, {%2, [[1, 2, 5, 3, 4], [1, 1, 1, 1]]}, {%2, [[2, 3, 1, 4, 5], [1, 1, 1, 1]]}, {%2, [[3, 1, 2, 4, 5], [1, 1, 1, 1]]}}, " the pattern set ", {%1, [[5, 4, 1, 3, 2], [1, 1, 1, 1]]}, " has scheme:" %1 := [[1, 2, 3], [1, 1]] %2 := [[3, 2, 1], [1, 1]] {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {[0, 2, 0, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, %1], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 2, 0, 0], [0, 1, 1, 0, 0], [0, 2, 0, 0, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1}, %1], [[3, 2, 1, 4], {}, {[0, 0, 0, 0, 1], [0, 2, 0, 0, 0]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1], [0, 2, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, %1], [[4, 2, 1, 3], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 2, 0, 0, 0]}], [ [4, 2, 3, 1], {2, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 2, 0, 0], [0, 1, 1, 0, 0], [0, 2, 0, 0, 0]}], [[4, 3, 1, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {[0, 0, 2, 0, 0], [0, 1, 1, 0, 0], [0, 2, 0, 0, 0]}], [[3, 2, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 1, 5, 4], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 2, 0, 0, 0, 0]}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 2, 0, 0, 0, 0]}], [ [4, 2, 1, 5, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 2, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {1, 2}, { [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 2, 0, 0, 0, 0]}], [[4, 3, 1, 5, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 3, 2, 5, 1], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 2, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 2, 0, 0, 0, 0]}], [ [4, 3, 5, 1, 2], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [ [4, 3, 5, 2, 1], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 2, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 2, 0, 0, 0, 0]}]} %1 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 116, 307, 760, 1779, 3986, 8641, 18282, 38005, 78024, 158791, 321236, 647247, 1300630, 2609029, 5227766] "" "Class ", 7396, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 1, 1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 4, 5, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 3, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 2, 1, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 5, 4, 2, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 1, 1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2, 4, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 4, 5, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 2, 5, 3, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 4, 2, 1, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 5, 4, 2, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 2], [0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7397, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 1, 1, 1]]}, {[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 4, 5, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 3, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 3, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 2, 1, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 5, 4, 3, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 5, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 1, 1, 1]]}, {[[1, 3, 2], [1, 1]], [[4, 1, 2, 3, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 4, 5, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 3, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 3, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 2, 1, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 5, 4, 3, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 5, 1], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7398, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [1, 1, 1, 1]]}, {[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 4, 5, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [1, 1, 1, 1]]} {[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 5, 1], [1, 1, 1, 1]]}, {[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 4, 5, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 5, 4, 3, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1, 5], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 1, 2, 3, 4], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 0, 2, 0], [0, 1, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7399, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [1, 1, 1, 1]]}, {[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 5, 4, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 4, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 2, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 1, 2, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 5, 3, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [1, 1, 1, 1]]}, {[[1, 3, 2], [1, 1]], [[4, 2, 1, 3, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 3, 5, 4, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 2, 4, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 4, 2, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 3, 1, 2, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 5, 3, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1, 5], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7400, " is:" {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [1, 1, 1, 1]]}, {[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 5, 4, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 4, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 2, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 5, 3, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 1, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [1, 1, 1, 1]]} {[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 5, 1], [1, 1, 1, 1]]}, {[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 5, 4, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 2, 4, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 4, 2, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 5, 3, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 4, 2, 1, 5], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 2, 1, 3, 4], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {[0, 0, 2, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7401, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [1, 1, 1, 1]]}, {[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 3, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 2, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 4, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 3, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 5, 4, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 5, 1], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [1, 1, 1, 1]]}, {[[1, 3, 2], [1, 1]], [[4, 3, 1, 2, 5], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 4, 5, 3, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[1, 5, 4, 2, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 1, 2, 4, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[5, 2, 1, 3, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 5, 4, 1], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 5, 1], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1, 5], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [3, 4, 1, 2, 5], {3, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1033, 2986, 8594, 24674, 70757, 202814, 581272, 1666003, 4775323, 13688536, 39240095, 112490042, 322480613] "" "Class ", 7402, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 1, 1, 1]]}, {[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 4, 5, 3, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 2, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 4, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 2, 1, 3, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 5, 4, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 1, 1, 1]]}, {[[1, 3, 2], [1, 1]], [[5, 3, 1, 2, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 4, 5, 3, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 2, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 4, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 2, 1, 3, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 5, 4, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1, 5], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 2, 5, 1], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [ [2, 3, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3, 4}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7403, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [1, 1, 1, 1]]}, {[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 1, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 2, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 4, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 5, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 5, 4, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 5, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [1, 1, 1, 1]]}, {[[1, 3, 2], [1, 1]], [[4, 5, 1, 2, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 1, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 2, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 4, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 5, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 5, 4, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 5, 4], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 5, 1, 2], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, %1], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {3}, %1], [[2, 3, 4, 1], {4}, %1], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} %1 := {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7404, " is:" {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 1, 1, 1]]}, {[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 2, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 4, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 5, 4, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 1, 1, 1]]}, {[[1, 3, 2], [1, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 4, 5, 2, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 2, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 4, 3], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 5, 4, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4, 5], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[3, 4, 5, 2, 1], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [ [2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1032, 2973, 8496, 24111, 68017, 190885, 533294, 1484021, 4115186, 11375765, 31358377, 86223943, 236540916] "" "Class ", 7405, " is:" {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 5, 1], [1, 1, 1, 1]]}, {[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 3, 4, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 3, 4, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 3, 2, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 5, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 3, 1, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 2, 3, 5, 1], [1, 1, 1, 1]]} {[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 5, 1], [1, 1, 1, 1]]}, {[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 3, 4, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 3, 4, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 3, 2, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 4, 3, 5, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 4, 3, 1, 5], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 2, 3, 1, 4], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7406, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [1, 1, 1, 1]]}, {[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 4, 3, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 3, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 3, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 5, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [1, 1, 1, 1]]}, {[[1, 3, 2], [1, 1]], [[5, 3, 2, 1, 4], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 5, 4, 3, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 1, 4, 3, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 5, 2, 3, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 4, 5, 2], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1, 5], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 2, 5, 1], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 2, 1, 3], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 356, 1044, 3057, 8948, 26192, 76674, 224465, 657137, 1923817, 5632105, 16488346, 48270655, 141315320, 413709331] "" "Class ", 7407, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [1, 1, 1, 1]]}, {[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 1, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 3, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 3, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 5, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 5, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 5, 4], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [1, 1, 1, 1]]}, {[[1, 3, 2], [1, 1]], [[4, 5, 2, 1, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 1, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 1, 3, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 5, 3, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 5, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 5, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 5, 4], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 5, 1, 2], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734] "" "Class ", 7408, " is:" {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 1, 1, 1]]}, {[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 2, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 3, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 5, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 1, 1, 1]]}, {[[1, 3, 2], [1, 1]], [[5, 4, 2, 1, 3], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 5, 4, 2, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 1, 3, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 5, 3, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 5, 3], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4, 5], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 3, 5, 2, 1], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 355, 1032, 2973, 8496, 24111, 68017, 190885, 533294, 1484021, 4115186, 11375765, 31358377, 86223943, 236540916] "" "Class ", 7409, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [1, 1, 1, 1]]}, {[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 2, 3, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 1, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 5, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 5, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [1, 1, 1, 1]]}, {[[1, 3, 2], [1, 1]], [[5, 3, 4, 1, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 2, 3, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 1, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 5, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 5, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3, 5], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 2, 3, 1], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 121, 354, 1021, 2901, 8130, 22513, 61713, 167746, 452789, 1215197, 3246050, 8637641, 22912633, 60624546, 160075117] "" "Class ", 7410, " is:" {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 1, 1]]}, {[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 5, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 5, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 1, 1]]}, {[[1, 3, 2], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 3, 1, 2], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 3, 5, 4], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 3, 5, 4], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4, 5], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[4, 5, 3, 2, 1], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 119, 334, 902, 2351, 5945, 14660, 35408, 84061, 196715, 454778, 1040522, 2359451, 5308589, 11862208, 26345684] "" "Class ", 7411, " is:" {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]}, {[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 2, 3, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4, 5], [1, 1, 1, 1]]}} {[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]}, {[[1, 3, 2], [1, 1]], [[5, 4, 2, 3, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]}, {[[2, 1, 3], [1, 1]], [[5, 4, 2, 3, 1], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3, 5], [1, 1, 1, 1]]}, {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3, 5], [1, 1, 1, 1]]}, {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4, 5], [1, 1, 1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[5, 3, 4, 2, 1], [1, 1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3}, {[0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 41, 119, 334, 902, 2351, 5945, 14660, 35408, 84061, 196715, 454778, 1040522, 2359451, 5308589, 11862208, 26345684] "" "Out of the ", 7411, " equivalence classes ", 2465, "(or ", 33.26136824, " %) classes have enumeration schemes." 4946, "(or ", 66.73863176, " %) classes do not have enumeration schemes of depth <=", 5, ", with gap vectors of weight <=", 2 "The classes that failed are: " {{{%1356, %355}}, {{%1356, %1168}}, {{%1356, %1131}}, {{%1356, %1128}}, {{%1356, %1318}}, {{%1356, %1108}}, {{%1356, %981}}, {{%1356, %1295}}, {{%1356, %974}}, {{%1356, %1236}}, {{%1356, %714}}, {{%1356, %563}}, {{%1356, %1207}}, {{%1356, %556}}, {{%1356, %60}}, {{%1356, %479}}, {{%1356, %366}}, {{%1356, %1319}}, {{%2, %563}}, {{%2, %1207}}, {{%2, %556}}, {{%2, [[5, 4, 3, 2, 1], [0, 0, 0, 0]]}}, {{%2, %366}}, {{%2, %1319}}, {{%1356, %353}, {%1356, %354}}, {{%1356, %351}, {%1356, %352}}, {{%1356, %1172}, {%1356, %1171}}, { {%1356, [[1, 2, 3, 5, 4], [0, 1, 0, 0]]}, {%1356, [[2, 1, 3, 4, 5], [0, 0, 1, 0]]}}, {{%1356, %347}, {%1356, %348}}, {{%1356, %349}, {%1356, %350}}, {{%1356, %345}, {%1356, %346}}, {{%1356, %1165}, {%1356, %1164}}, {{%1356, %1122}, {%1356, %1123}}, {{%1356, %1118}, {%1356, %1119}}, {{%1356, %1120}, {%1356, %1121}}, {{%1356, %1116}, {%1356, %1117}}, { {%1356, [[1, 2, 4, 3, 5], [0, 1, 0, 0]]}, {%1356, [[1, 3, 2, 4, 5], [0, 0, 1, 0]]}}, { {%1356, [[1, 2, 4, 3, 5], [0, 1, 0, 1]]}, {%1356, [[1, 3, 2, 4, 5], [1, 0, 1, 0]]}}, {{%1356, %1158}, {%1356, %1159}}, {{%1356, %1150}, {%1356, %1151}}, {{%1356, %1160}, {%1356, %1161}}, {{%1356, %1152}, {%1356, %1153}}, { {%1356, [[1, 2, 4, 3, 5], [1, 1, 0, 0]]}, {%1356, [[1, 3, 2, 4, 5], [0, 0, 1, 1]]}}, {{%1356, %1352}, {%1356, %1353}}, {{%1356, %1156}, {%1356, %1157}}, {{%1356, %1148}, {%1356, %1149}}, {{%1356, %323}, {%1356, %324}}, {{%1356, %313}, {%1356, %314}}, {{%1356, %317}, {%1356, %318}}, {{%1356, %307}, {%1356, %308}}, {{%1356, %319}, {%1356, %320}}, {{%1356, %309}, {%1356, %310}}, {{%1356, %968}, {%1356, %969}}, {{%1356, %966}, {%1356, %967}}, {{%1356, %315}, {%1356, %316}}, {{%1356, %964}, {%1356, %965}}, { {%1356, [[1, 2, 5, 3, 4], [0, 1, 0, 0]]}, {%1356, [[2, 3, 1, 4, 5], [0, 0, 1, 0]]}}, {{%1356, %1316}, {%1356, %1317}}, {{%1356, %1076}, {%1356, %1077}}, {{%1356, %1070}, {%1356, %1071}}, {{%1356, %341}, {%1356, %342}}, {{%1356, %1072}, {%1356, %1073}}, {{%1356, %1338}, {%1356, %1339}}, {{%1356, %1314}, {%1356, %1315}}, {{%1356, %1074}, {%1356, %1075}}, {{%1356, %1068}, {%1356, %1069}}, { {%1356, [[1, 2, 5, 4, 3], [0, 1, 0, 0]]}, {%1356, [[3, 2, 1, 4, 5], [0, 0, 1, 0]]}}, { {%1356, [[1, 2, 5, 4, 3], [0, 1, 0, 1]]}, {%1356, [[3, 2, 1, 4, 5], [1, 0, 1, 0]]}}, {{%1356, %906}, {%1356, %907}}, {{%1356, %900}, {%1356, %901}}, {{%1356, %303}, {%1356, %304}}, {{%1356, %299}, {%1356, %300}}, {{%1356, %908}, {%1356, %909}}, {{%1356, %904}, {%1356, %905}}, {{%1356, %898}, {%1356, %899}}, { {%1356, [[1, 3, 2, 5, 4], [0, 0, 1, 1]]}, {%1356, [[2, 1, 4, 3, 5], [1, 1, 0, 0]]}}, { {%1356, [[1, 3, 2, 5, 4], [0, 1, 0, 0]]}, {%1356, [[2, 1, 4, 3, 5], [0, 0, 1, 0]]}}, {{%1356, %1100}, {%1356, %1101}}, {{%1356, %1104}, {%1356, %1105}}, {{%1356, %1096}, {%1356, %1097}}, {{%1356, %1342}, {%1356, %1343}}, {{%1356, %1106}, {%1356, %1107}}, {{%1356, %1098}, {%1356, %1099}}, {{%1356, %1102}, {%1356, %1103}}, {{%1356, %1094}, {%1356, %1095}}, { {%1356, [[1, 3, 4, 2, 5], [0, 1, 0, 0]]}, {%1356, [[1, 4, 2, 3, 5], [0, 0, 1, 0]]}}, {{%1356, %1350}, {%1356, %1351}}, {{%1356, %1142}, {%1356, %1143}}, {{%1356, %1134}, {%1356, %1135}}, {{%1356, %1144}, {%1356, %1145}}, {{%1356, %1136}, {%1356, %1137}}, { {%1356, [[1, 3, 4, 2, 5], [1, 1, 0, 0]]}, {%1356, [[1, 4, 2, 3, 5], [0, 0, 1, 1]]}}, {{%1356, %1348}, {%1356, %1349}}, {{%1356, %1140}, {%1356, %1141}}, {{%1356, %1132}, {%1356, %1133}}, {{%1356, %241}, {%1356, %242}}, {{%1356, %231}, {%1356, %232}}, {{%1356, %235}, {%1356, %236}}, {{%1356, %225}, {%1356, %226}}, {{%1356, %237}, {%1356, %238}}, {{%1356, %227}, {%1356, %228}}, {{%1356, %758}, {%1356, %759}}, {{%1356, %756}, {%1356, %757}}, {{%1356, %233}, {%1356, %234}}, {{%1356, %754}, {%1356, %755}}, {{%1356, %1052}, {%1356, %1053}}, {{%1356, %1040}, {%1356, %1041}}, {{%1356, %1044}, {%1356, %1045}}, {{%1356, %1032}, {%1356, %1033}}, {{%1356, %1046}, {%1356, %1047}}, {{%1356, %1034}, {%1356, %1035}}, {{%1356, %1050}, {%1356, %1051}}, {{%1356, %1038}, {%1356, %1039}}, {{%1356, %1042}, {%1356, %1043}}, {{%1356, %1030}, {%1356, %1031}}, {{%1356, %223}, {%1356, %224}}, {{%1356, %215}, {%1356, %216}}, {{%1356, %217}, {%1356, %218}}, {{%1356, %211}, {%1356, %212}}, {{%1356, %219}, {%1356, %220}}, {{%1356, %686}, {%1356, %687}}, {{%1356, %692}, {%1356, %693}}, {{%1356, %688}, {%1356, %689}}, {{%1356, %690}, {%1356, %691}}, {{%1356, %684}, {%1356, %685}}, {{%1356, %1285}, {%1356, %1286}}, {{%1356, %1281}, {%1356, %1282}}, { {%1356, [[1, 4, 2, 5, 3], [0, 1, 0, 0]]}, {%1356, [[3, 1, 4, 2, 5], [0, 0, 1, 0]]}}, {{%1356, %942}, {%1356, %943}}, {{%1356, %946}, {%1356, %947}}, {{%1356, %938}, {%1356, %939}}, {{%1356, %1283}, {%1356, %1284}}, {{%1356, %1279}, {%1356, %1280}}, {{%1356, %948}, {%1356, %949}}, {{%1356, %940}, {%1356, %941}}, {{%1356, %944}, {%1356, %945}}, {{%1356, %936}, {%1356, %937}}, { {%1356, [[1, 4, 3, 2, 5], [0, 0, 1, 0]]}, {%1356, [[1, 4, 3, 2, 5], [0, 1, 0, 0]]}}, { {%1356, [[1, 4, 3, 2, 5], [0, 0, 1, 1]]}, {%1356, [[1, 4, 3, 2, 5], [1, 1, 0, 0]]}}, {{%1356, %1346}, {%1356, %1347}}, {{%1356, %1129}, {%1356, %1130}}, {{%1356, %1344}, {%1356, %1345}}, {{%1356, %1245}, {%1356, %1246}}, {{%1356, %1241}, {%1356, %1242}}, {{%1356, %738}, {%1356, %739}}, {{%1356, %730}, {%1356, %731}}, {{%1356, %734}, {%1356, %735}}, {{%1356, %726}, {%1356, %727}}, {{%1356, %1243}, {%1356, %1244}}, {{%1356, %1239}, {%1356, %1240}}, {{%1356, %736}, {%1356, %737}}, {{%1356, %728}, {%1356, %729}}, {{%1356, %732}, {%1356, %733}}, {{%1356, %724}, {%1356, %725}}, {{%1356, %273}, {%1356, %274}}, {{%1356, %267}, {%1356, %268}}, {{%1356, %269}, {%1356, %270}}, {{%1356, %263}, {%1356, %264}}, {{%1356, %848}, {%1356, %849}}, {{%1356, %842}, {%1356, %843}}, {{%1356, %850}, {%1356, %851}}, {{%1356, %844}, {%1356, %845}}, {{%1356, %846}, {%1356, %847}}, {{%1356, %840}, {%1356, %841}}, {{%1356, %165}, {%1356, %166}}, {{%1356, %157}, {%1356, %158}}, {{%1356, %159}, {%1356, %160}}, {{%1356, %151}, {%1356, %152}}, {{%1356, %161}, {%1356, %162}}, {{%1356, %632}, {%1356, %633}}, {{%1356, %636}, {%1356, %637}}, {{%1356, %155}, {%1356, %156}}, {{%1356, %634}, {%1356, %635}}, {{%1356, %630}, {%1356, %631}}, {{%1356, %1310}, {%1356, %1311}}, {{%1356, %1306}, {%1356, %1307}}, {{%1356, %333}, {%1356, %334}}, {{%1356, %335}, {%1356, %336}}, {{%1356, %331}, {%1356, %332}}, {{%1356, %1308}, {%1356, %1309}}, {{%1356, %1304}, {%1356, %1305}}, {{%1356, %1127}, {%1356, %1126}}, {{%1356, %1056}, {%1356, %1057}}, {{%1356, %1054}, {%1356, %1055}}, {{%1356, %1273}, {%1356, %1274}}, {{%1356, %1269}, {%1356, %1270}}, {{%1356, %297}, {%1356, %298}}, {{%1356, %293}, {%1356, %294}}, {{%1356, %295}, {%1356, %296}}, {{%1356, %289}, {%1356, %290}}, {{%1356, %1271}, {%1356, %1272}}, {{%1356, %1267}, {%1356, %1268}}, { {%1356, [[1, 5, 2, 4, 3], [1, 1, 0, 0]]}, {%1356, [[3, 2, 4, 1, 5], [0, 0, 1, 1]]}}, {{%1356, %291}, {%1356, %292}}, {{%1356, %882}, {%1356, %883}}, {{%1356, %1125}, {%1356, %1124}}, {{%1356, %1024}, {%1356, %1025}}, {{%1356, %1016}, {%1356, %1017}}, { {%1356, [[1, 5, 3, 2, 4], [0, 1, 0, 0]]}, {%1356, [[2, 4, 3, 1, 5], [0, 0, 1, 0]]}}, {{%1356, %1302}, {%1356, %1303}}, {{%1356, %1020}, {%1356, %1021}}, {{%1356, %1012}, {%1356, %1013}}, {{%1356, %1022}, {%1356, %1023}}, {{%1356, %1014}, {%1356, %1015}}, { {%1356, [[1, 5, 3, 2, 4], [1, 1, 0, 0]]}, {%1356, [[2, 4, 3, 1, 5], [0, 0, 1, 1]]}}, {{%1356, %1300}, {%1356, %1301}}, {{%1356, %1018}, {%1356, %1019}}, {{%1356, %1010}, {%1356, %1011}}, {{%1356, %207}, {%1356, %208}}, {{%1356, %195}, {%1356, %196}}, {{%1356, %209}, {%1356, %210}}, {{%1356, %199}, {%1356, %200}}, {{%1356, %203}, {%1356, %204}}, {{%1356, %191}, {%1356, %192}}, {{%1356, %205}, {%1356, %206}}, {{%1356, %193}, {%1356, %194}}, { {%1356, [[1, 5, 3, 4, 2], [1, 1, 0, 0]]}, {%1356, [[4, 2, 3, 1, 5], [0, 0, 1, 1]]}}, {{%1356, %197}, {%1356, %198}}, {{%1356, %201}, {%1356, %202}}, {{%1356, %189}, {%1356, %190}}, {{%1356, %259}, {%1356, %260}}, {{%1356, %253}, {%1356, %254}}, {{%1356, %261}, {%1356, %262}}, {{%1356, %255}, {%1356, %256}}, {{%1356, %257}, {%1356, %258}}, {{%1356, %251}, {%1356, %252}}, {{%1356, %832}, {%1356, %833}}, {{%1356, %828}, {%1356, %829}}, {{%1356, %1330}, {%1356, %1331}}, {{%1356, %1259}, {%1356, %1260}}, {{%1356, %830}, {%1356, %831}}, {{%1356, %826}, {%1356, %827}}, {{%1356, %147}, {%1356, %148}}, {{%1356, %141}, {%1356, %142}}, {{%1356, %149}, {%1356, %150}}, {{%1356, %143}, {%1356, %144}}, {{%1356, %145}, {%1356, %146}}, {{%1356, %139}, {%1356, %140}}, {{%1356, %614}, {%1356, %615}}, {{%1356, %610}, {%1356, %611}}, {{%1356, %1326}, {%1356, %1327}}, {{%1356, %1324}, {%1356, %1325}}, {{%1356, %612}, {%1356, %613}}, {{%1356, %608}, {%1356, %609}}, {{%1356, %1115}, {%1356, %1114}}, {{%1356, %1113}, {%1356, %1112}}, {{%1356, %1109}, {%1356, %1110}}, { {%1356, [[2, 1, 4, 5, 3], [0, 0, 1, 0]]}, {%1356, [[3, 1, 2, 5, 4], [0, 1, 0, 0]]}}, {{%1356, %1093}, {%1356, %1092}}, {{%1356, %1289}, {%1356, %1290}}, {{%1356, %1287}, {%1356, %1288}}, {{%1356, %1091}, {%1356, %1090}}, {{%1356, %960}, {%1356, %961}}, {{%1356, %952}, {%1356, %953}}, {{%1356, %962}, {%1356, %963}}, {{%1356, %954}, {%1356, %955}}, {{%1356, %958}, {%1356, %959}}, {{%1356, %950}, {%1356, %951}}, {{%1356, %1089}, {%1356, %1088}}, {{%1356, %1087}, {%1356, %1086}}, {{%1356, %1085}, {%1356, %1084}}, {{%1356, %1083}, {%1356, %1082}}, { {%1356, [[2, 1, 5, 3, 4], [1, 0, 0, 1]]}, {%1356, [[2, 3, 1, 5, 4], [1, 0, 0, 1]]}}, {{%1356, %1066}, {%1356, %1067}}, {{%1356, %1062}, {%1356, %1063}}, {{%1356, %1336}, {%1356, %1337}}, {{%1356, %1312}, {%1356, %1313}}, {{%1356, %1064}, {%1356, %1065}}, {{%1356, 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2], [1, 0, 0, 1]]}}, {{%9, %232}, {%7, %231}}, {{%9, %230}, {%7, %229}}, {{%9, %228}, {%7, %227}}, {{%9, %226}, {%7, %225}}, {{%9, %224}, {%7, %223}}, {{%9, %222}, {%7, %221}}, {{%9, %220}, {%7, %219}}, {{%9, %218}, {%7, %217}}, {{%9, [[4, 2, 1, 3, 5], [1, 0, 0, 0]]}, {%7, [[1, 3, 5, 4, 2], [0, 0, 0, 1]]}}, { {%9, [[4, 2, 1, 3, 5], [1, 0, 0, 1]]}, {%7, [[1, 3, 5, 4, 2], [1, 0, 0, 1]]}}, {{%9, %216}, {%7, %215}}, {{%9, %214}, {%7, %213}}, {{%9, %212}, {%7, %211}}, {{%9, %210}, {%7, %209}}, {{%9, %208}, {%7, %207}}, {{%9, %206}, {%7, %205}}, {{%9, %204}, {%7, %203}}, {{%9, %202}, {%7, %201}}, {{%9, [[4, 2, 3, 1, 5], [1, 0, 0, 0]]}, {%7, [[1, 5, 3, 4, 2], [0, 0, 0, 1]]}}, { {%9, [[4, 2, 3, 1, 5], [1, 0, 0, 1]]}, {%7, [[1, 5, 3, 4, 2], [1, 0, 0, 1]]}}, {{%9, %200}, {%7, %199}}, {{%9, %198}, {%7, %197}}, {{%9, %196}, {%7, %195}}, {{%9, %194}, {%7, %193}}, {{%9, %192}, {%7, %191}}, {{%9, %190}, {%7, %189}}, {{%9, %188}, {%7, %187}}, {{%9, %186}, {%7, %185}}, {{%9, %184}, {%7, %183}}, {{%9, %182}, {%7, %181}}, {{%9, %180}, {%7, %179}}, {{%9, %178}, {%7, %177}}, {{%9, [[4, 2, 3, 5, 1], [1, 0, 0, 0]]}, {%7, [[5, 1, 3, 4, 2], [0, 0, 0, 1]]}}, { {%9, [[4, 2, 3, 5, 1], [1, 0, 0, 1]]}, {%7, [[5, 1, 3, 4, 2], [1, 0, 0, 1]]}}, {{%9, %176}, {%7, %175}}, {{%9, %174}, {%7, %173}}, {{%9, %172}, {%7, %171}}, {{%9, %170}, {%7, %169}}, {{%9, %168}, {%7, %167}}, {{%9, %166}, {%7, %165}}, {{%9, %164}, {%7, %163}}, {{%9, %162}, {%7, %161}}, {{%9, %160}, {%7, %159}}, { {%9, [[4, 3, 1, 2, 5], [1, 0, 0, 0]]}, {%7, [[1, 4, 5, 3, 2], [0, 0, 0, 1]]}}, { {%9, [[4, 3, 1, 2, 5], [1, 0, 0, 1]]}, {%7, [[1, 4, 5, 3, 2], [1, 0, 0, 1]]}}, {{%9, %158}, {%7, %157}}, {{%9, %156}, {%7, %155}}, {{%9, %154}, {%7, %153}}, {{%9, %152}, {%7, %151}}, {{%9, %150}, {%7, %149}}, {{%9, %148}, {%7, %147}}, {{%9, %146}, {%7, %145}}, { {%9, [[4, 3, 2, 1, 5], [1, 0, 0, 0]]}, {%7, [[1, 5, 4, 3, 2], [0, 0, 0, 1]]}}, { {%9, [[4, 3, 2, 1, 5], [1, 0, 0, 1]]}, {%7, [[1, 5, 4, 3, 2], [1, 0, 0, 1]]}}, {{%9, %144}, {%7, %143}}, {{%9, %142}, {%7, %141}}, {{%9, %140}, {%7, %139}}, {{%9, %138}, {%7, %137}}, {{%9, %136}, {%7, %135}}, { {%9, [[4, 3, 2, 5, 1], [1, 0, 0, 0]]}, {%7, [[5, 1, 4, 3, 2], [0, 0, 0, 1]]}}, { {%9, [[4, 3, 2, 5, 1], [1, 0, 0, 1]]}, {%7, [[5, 1, 4, 3, 2], [1, 0, 0, 1]]}}, {{%9, %134}, {%7, %133}}, {{%9, %132}, {%7, %131}}, {{%9, [[4, 3, 5, 1, 2], [1, 0, 0, 0]]}, {%7, [[4, 5, 1, 3, 2], [0, 0, 0, 1]]}}, {{%9, %130}, {%7, %129}}, { {%9, [[4, 3, 5, 1, 2], [1, 0, 1, 0]]}, {%7, [[4, 5, 1, 3, 2], [0, 1, 0, 1]]}}, {{%9, %128}, {%7, %127}}, { {%9, [[4, 3, 5, 2, 1], [1, 0, 0, 0]]}, {%7, [[5, 4, 1, 3, 2], [0, 0, 0, 1]]}}, { {%9, [[4, 3, 5, 2, 1], [1, 0, 0, 1]]}, {%7, [[5, 4, 1, 3, 2], [1, 0, 0, 1]]}}, {{%9, %126}, {%7, %125}}, {{%9, %124}, {%7, %123}}, {{%9, %122}, {%7, %121}}, {{%9, %120}, {%7, %119}}, {{%9, %118}, {%7, %117}}, {{%9, %116}, {%7, %115}}, {{%9, %114}, {%7, %113}}, {{%9, %112}, {%7, %111}}, {{%9, %110}, {%7, %109}}, {{%9, %108}, {%7, %107}}, {{%9, %106}, {%7, %105}}, {{%9, %104}, {%7, %103}}, {{%9, %102}, {%7, %101}}, {{%9, %100}, {%7, %99}}, {{%9, %98}, {%7, %97}}, {{%9, %96}, {%7, %95}}, {{%9, %94}, {%7, %93}}, {{%9, %92}, {%7, %91}}, {{%9, %90}, {%7, %89}}, {{%9, %88}, {%7, %87}}, {{%9, %86}, {%7, %85}}, {{%9, %84}, {%7, %83}}, {{%9, %82}, {%7, %81}}, {{%9, %80}, {%7, %79}}, {{%9, %78}, {%7, %77}}, {{%9, %76}, {%7, %75}}, {{%9, %74}, {%7, %73}}, {{%9, %72}, {%7, %71}}, {{%9, %70}, {%7, %69}}, {{%9, %68}, {%7, %67}}, {{%9, %63}, {%7, %64}}, {{%9, %66}, {%7, %65}}, {{%9, %64}, {%7, %63}}, {{%9, %62}, {%7, %61}}, {{%9, %60}, {%7, %60}}, {{%9, %59}, {%7, %58}}, {{%9, %57}, {%7, %56}}, {{%9, %55}, {%7, %54}}, {{%9, %53}, {%7, %52}}, {{%9, %51}, {%7, %50}}, {{%9, %49}, {%7, %48}}, {{%9, %47}, {%7, %46}}, {{%9, %45}, {%7, %44}}, {{%9, %43}, {%7, %42}}, {{%9, %41}, {%7, %40}}, {{%9, %39}, {%7, %38}}, {{%9, %37}, {%7, %36}}, {{%9, %35}, {%7, %34}}, {{%9, %33}, {%7, %32}}, {{%9, %31}, {%7, %30}}, {{%9, %29}, {%7, %28}}, {{%9, %27}, {%7, %26}}, {{%9, %25}, {%7, %24}}, {{%9, %23}, {%7, %22}}, {{%9, %21}, {%7, %20}}, {{%9, %19}, {%7, %18}}, {{%9, %17}, {%7, %16}}, {{%9, %15}, {%7, %14}}, {{%9, %13}, {%7, %12}}, {{%9, %11}, {%7, %10}}, {{%9, %8}, {%7, %6}}, {{%2, %5}, {%2, %4}, {%2, %3}, {%2, %1}}} %1 := [[4, 5, 2, 1, 3], [1, 1, 1, 1]] %2 := [[1, 2, 3], [1, 1]] %3 := [[4, 5, 1, 3, 2], [1, 1, 1, 1]] %4 := [[4, 3, 5, 1, 2], [1, 1, 1, 1]] %5 := [[3, 5, 4, 1, 2], [1, 1, 1, 1]] %6 := [[3, 5, 4, 2, 1], [0, 1, 1, 1]] %7 := [[2, 1, 3], [1, 1]] %8 := [[5, 4, 2, 1, 3], [1, 1, 1, 0]] %9 := [[1, 3, 2], [1, 1]] %10 := [[3, 5, 4, 2, 1], [0, 1, 0, 1]] %11 := [[5, 4, 2, 1, 3], [1, 0, 1, 0]] %12 := [[3, 5, 4, 2, 1], [0, 1, 1, 0]] %13 := [[5, 4, 2, 1, 3], [0, 1, 1, 0]] %14 := [[3, 5, 4, 2, 1], [0, 1, 0, 0]] %15 := [[5, 4, 2, 1, 3], [0, 0, 1, 0]] %16 := [[3, 4, 5, 2, 1], [0, 1, 0, 1]] %17 := [[5, 4, 1, 2, 3], [1, 0, 1, 0]] %18 := [[3, 4, 5, 2, 1], [0, 1, 0, 0]] %19 := [[5, 4, 1, 2, 3], [0, 0, 1, 0]] %20 := [[5, 2, 4, 3, 1], [1, 0, 1, 1]] %21 := [[5, 3, 2, 4, 1], [1, 1, 0, 1]] %22 := [[5, 2, 4, 3, 1], [0, 0, 1, 1]] %23 := [[5, 3, 2, 4, 1], [1, 1, 0, 0]] %24 := [[5, 2, 4, 3, 1], [1, 0, 1, 0]] %25 := [[5, 3, 2, 4, 1], [0, 1, 0, 1]] %26 := [[5, 2, 4, 3, 1], [0, 0, 1, 0]] %27 := [[5, 3, 2, 4, 1], [0, 1, 0, 0]] %28 := [[5, 2, 4, 3, 1], [1, 1, 0, 0]] %29 := [[5, 3, 2, 4, 1], [0, 0, 1, 1]] %30 := [[5, 2, 4, 3, 1], [0, 1, 0, 0]] %31 := [[5, 3, 2, 4, 1], [0, 0, 1, 0]] %32 := [[2, 5, 4, 3, 1], [0, 1, 1, 1]] %33 := [[5, 3, 2, 1, 4], [1, 1, 1, 0]] %34 := [[2, 5, 4, 3, 1], [0, 0, 1, 1]] %35 := [[5, 3, 2, 1, 4], [1, 1, 0, 0]] %36 := [[2, 5, 4, 3, 1], [0, 1, 0, 1]] %37 := [[5, 3, 2, 1, 4], [1, 0, 1, 0]] %38 := [[2, 5, 4, 3, 1], [0, 1, 1, 0]] %39 := [[5, 3, 2, 1, 4], [0, 1, 1, 0]] %40 := [[2, 5, 4, 3, 1], [0, 0, 1, 0]] %41 := [[5, 3, 2, 1, 4], [0, 1, 0, 0]] %42 := [[2, 5, 4, 3, 1], [0, 1, 0, 0]] %43 := [[5, 3, 2, 1, 4], [0, 0, 1, 0]] %44 := [[2, 4, 5, 3, 1], [0, 1, 1, 1]] %45 := [[5, 3, 1, 2, 4], [1, 1, 1, 0]] %46 := [[2, 4, 5, 3, 1], [0, 0, 1, 1]] %47 := [[5, 3, 1, 2, 4], [1, 1, 0, 0]] %48 := [[2, 4, 5, 3, 1], [0, 1, 0, 1]] %49 := [[5, 3, 1, 2, 4], [1, 0, 1, 0]] %50 := [[2, 4, 5, 3, 1], [0, 1, 1, 0]] %51 := [[5, 3, 1, 2, 4], [0, 1, 1, 0]] %52 := [[2, 4, 5, 3, 1], [1, 0, 1, 0]] %53 := [[5, 3, 1, 2, 4], [0, 1, 0, 1]] %54 := [[2, 4, 5, 3, 1], [0, 0, 1, 0]] %55 := [[5, 3, 1, 2, 4], [0, 1, 0, 0]] %56 := [[2, 4, 5, 3, 1], [0, 1, 0, 0]] %57 := [[5, 3, 1, 2, 4], [0, 0, 1, 0]] %58 := [[5, 2, 3, 4, 1], [1, 1, 1, 0]] %59 := [[5, 2, 3, 4, 1], [0, 1, 1, 1]] %60 := [[5, 2, 3, 4, 1], [0, 1, 1, 0]] %61 := [[5, 2, 3, 4, 1], [1, 0, 1, 0]] %62 := [[5, 2, 3, 4, 1], [0, 1, 0, 1]] %63 := [[5, 2, 3, 4, 1], [0, 0, 1, 0]] %64 := [[5, 2, 3, 4, 1], [0, 1, 0, 0]] %65 := [[5, 2, 3, 4, 1], [1, 1, 0, 0]] %66 := [[5, 2, 3, 4, 1], [0, 0, 1, 1]] %67 := [[2, 5, 3, 4, 1], [0, 1, 1, 1]] %68 := [[5, 2, 3, 1, 4], [1, 1, 1, 0]] %69 := [[2, 5, 3, 4, 1], [0, 1, 0, 1]] %70 := [[5, 2, 3, 1, 4], [1, 0, 1, 0]] %71 := [[2, 5, 3, 4, 1], [1, 1, 1, 0]] %72 := [[5, 2, 3, 1, 4], [0, 1, 1, 1]] %73 := [[2, 5, 3, 4, 1], [0, 1, 1, 0]] %74 := [[5, 2, 3, 1, 4], [0, 1, 1, 0]] %75 := [[2, 5, 3, 4, 1], [1, 0, 1, 0]] %76 := [[5, 2, 3, 1, 4], [0, 1, 0, 1]] %77 := [[2, 5, 3, 4, 1], [0, 0, 1, 0]] %78 := [[5, 2, 3, 1, 4], [0, 1, 0, 0]] %79 := [[2, 5, 3, 4, 1], [0, 1, 0, 0]] %80 := [[5, 2, 3, 1, 4], [0, 0, 1, 0]] %81 := [[2, 3, 5, 4, 1], [1, 0, 1, 1]] %82 := [[5, 2, 1, 3, 4], [1, 1, 0, 1]] %83 := [[2, 3, 5, 4, 1], [0, 0, 1, 1]] %84 := [[5, 2, 1, 3, 4], [1, 1, 0, 0]] %85 := [[2, 3, 5, 4, 1], [0, 1, 1, 0]] %86 := [[5, 2, 1, 3, 4], [0, 1, 1, 0]] %87 := [[2, 3, 5, 4, 1], [1, 0, 1, 0]] %88 := [[5, 2, 1, 3, 4], [0, 1, 0, 1]] %89 := [[2, 3, 5, 4, 1], [0, 0, 1, 0]] %90 := [[5, 2, 1, 3, 4], [0, 1, 0, 0]] %91 := [[2, 3, 5, 4, 1], [0, 1, 0, 0]] %92 := [[5, 2, 1, 3, 4], [0, 0, 1, 0]] %93 := [[2, 3, 4, 5, 1], [1, 1, 1, 0]] %94 := [[5, 1, 2, 3, 4], [0, 1, 1, 1]] %95 := [[2, 3, 4, 5, 1], [0, 1, 1, 0]] %96 := [[5, 1, 2, 3, 4], [0, 1, 1, 0]] %97 := [[2, 3, 4, 5, 1], [1, 0, 1, 0]] %98 := [[5, 1, 2, 3, 4], [0, 1, 0, 1]] %99 := [[2, 3, 4, 5, 1], [0, 0, 1, 0]] %100 := [[5, 1, 2, 3, 4], [0, 1, 0, 0]] %101 := [[2, 3, 4, 5, 1], [0, 1, 0, 0]] %102 := [[5, 1, 2, 3, 4], [0, 0, 1, 0]] %103 := [[5, 3, 4, 1, 2], [1, 1, 0, 1]] %104 := [[4, 5, 2, 3, 1], [1, 0, 1, 1]] %105 := [[5, 3, 4, 1, 2], [0, 1, 0, 1]] %106 := [[4, 5, 2, 3, 1], [1, 0, 1, 0]] %107 := [[5, 3, 4, 1, 2], [1, 1, 0, 0]] %108 := [[4, 5, 2, 3, 1], [0, 0, 1, 1]] %109 := [[5, 3, 4, 1, 2], [0, 1, 0, 0]] %110 := [[4, 5, 2, 3, 1], [0, 0, 1, 0]] %111 := [[3, 5, 4, 1, 2], [0, 1, 1, 1]] %112 := [[4, 5, 2, 1, 3], [1, 1, 1, 0]] %113 := [[3, 5, 4, 1, 2], [0, 1, 0, 1]] %114 := [[4, 5, 2, 1, 3], [1, 0, 1, 0]] %115 := [[3, 5, 4, 1, 2], [0, 1, 1, 0]] %116 := [[4, 5, 2, 1, 3], [0, 1, 1, 0]] %117 := [[3, 5, 4, 1, 2], [0, 1, 0, 0]] %118 := [[4, 5, 2, 1, 3], [0, 0, 1, 0]] %119 := [[3, 4, 5, 1, 2], [0, 1, 0, 1]] %120 := [[4, 5, 1, 2, 3], [1, 0, 1, 0]] %121 := [[3, 4, 5, 1, 2], [0, 1, 0, 0]] %122 := [[4, 5, 1, 2, 3], [0, 0, 1, 0]] %123 := [[5, 4, 1, 3, 2], [1, 1, 0, 1]] %124 := [[4, 3, 5, 2, 1], [1, 0, 1, 1]] %125 := [[5, 4, 1, 3, 2], [0, 1, 0, 1]] %126 := [[4, 3, 5, 2, 1], [1, 0, 1, 0]] %127 := [[4, 5, 1, 3, 2], [1, 1, 0, 1]] %128 := [[4, 3, 5, 1, 2], [1, 0, 1, 1]] %129 := [[4, 5, 1, 3, 2], [1, 0, 0, 1]] %130 := [[4, 3, 5, 1, 2], [1, 0, 0, 1]] %131 := [[5, 1, 4, 3, 2], [1, 0, 1, 1]] %132 := [[4, 3, 2, 5, 1], [1, 1, 0, 1]] %133 := [[5, 1, 4, 3, 2], [0, 0, 1, 1]] %134 := [[4, 3, 2, 5, 1], [1, 1, 0, 0]] %135 := [[5, 1, 4, 3, 2], [1, 0, 1, 0]] %136 := [[4, 3, 2, 5, 1], [0, 1, 0, 1]] %137 := [[5, 1, 4, 3, 2], [0, 0, 1, 0]] %138 := [[4, 3, 2, 5, 1], [0, 1, 0, 0]] %139 := [[1, 5, 4, 3, 2], [0, 1, 1, 1]] %140 := [[4, 3, 2, 1, 5], [1, 1, 1, 0]] %141 := [[1, 5, 4, 3, 2], [0, 0, 1, 1]] %142 := [[4, 3, 2, 1, 5], [1, 1, 0, 0]] %143 := [[1, 5, 4, 3, 2], [0, 1, 0, 1]] %144 := [[4, 3, 2, 1, 5], [1, 0, 1, 0]] %145 := [[1, 5, 4, 3, 2], [0, 1, 1, 0]] %146 := [[4, 3, 2, 1, 5], [0, 1, 1, 0]] %147 := [[1, 5, 4, 3, 2], [0, 0, 1, 0]] %148 := [[4, 3, 2, 1, 5], [0, 1, 0, 0]] %149 := [[1, 5, 4, 3, 2], [0, 1, 0, 0]] %150 := [[4, 3, 2, 1, 5], [0, 0, 1, 0]] %151 := [[1, 4, 5, 3, 2], [0, 1, 1, 1]] %152 := [[4, 3, 1, 2, 5], [1, 1, 1, 0]] %153 := [[1, 4, 5, 3, 2], [0, 0, 1, 1]] %154 := [[4, 3, 1, 2, 5], [1, 1, 0, 0]] %155 := [[1, 4, 5, 3, 2], [1, 1, 0, 1]] %156 := [[4, 3, 1, 2, 5], [1, 0, 1, 1]] %157 := [[1, 4, 5, 3, 2], [0, 1, 0, 1]] %158 := [[4, 3, 1, 2, 5], [1, 0, 1, 0]] %159 := [[1, 4, 5, 3, 2], [0, 1, 1, 0]] %160 := [[4, 3, 1, 2, 5], [0, 1, 1, 0]] %161 := [[1, 4, 5, 3, 2], [1, 0, 1, 0]] %162 := [[4, 3, 1, 2, 5], [0, 1, 0, 1]] %163 := [[1, 4, 5, 3, 2], [0, 0, 1, 0]] %164 := [[4, 3, 1, 2, 5], [0, 1, 0, 0]] %165 := [[1, 4, 5, 3, 2], [0, 1, 0, 0]] %166 := [[4, 3, 1, 2, 5], [0, 0, 1, 0]] %167 := [[5, 1, 3, 4, 2], [0, 1, 1, 1]] %168 := [[4, 2, 3, 5, 1], [1, 1, 1, 0]] %169 := [[5, 1, 3, 4, 2], [1, 0, 1, 1]] %170 := [[4, 2, 3, 5, 1], [1, 1, 0, 1]] %171 := [[5, 1, 3, 4, 2], [0, 0, 1, 1]] %172 := [[4, 2, 3, 5, 1], [1, 1, 0, 0]] %173 := [[5, 1, 3, 4, 2], [1, 1, 0, 1]] %174 := [[4, 2, 3, 5, 1], [1, 0, 1, 1]] %175 := [[5, 1, 3, 4, 2], [0, 1, 0, 1]] %176 := [[4, 2, 3, 5, 1], [1, 0, 1, 0]] %177 := [[5, 1, 3, 4, 2], [1, 1, 1, 0]] %178 := [[4, 2, 3, 5, 1], [0, 1, 1, 1]] %179 := [[5, 1, 3, 4, 2], [0, 1, 1, 0]] %180 := [[4, 2, 3, 5, 1], [0, 1, 1, 0]] %181 := [[5, 1, 3, 4, 2], [1, 0, 1, 0]] %182 := [[4, 2, 3, 5, 1], [0, 1, 0, 1]] %183 := [[5, 1, 3, 4, 2], [0, 0, 1, 0]] %184 := [[4, 2, 3, 5, 1], [0, 1, 0, 0]] %185 := [[5, 1, 3, 4, 2], [1, 1, 0, 0]] %186 := [[4, 2, 3, 5, 1], [0, 0, 1, 1]] %187 := [[5, 1, 3, 4, 2], [0, 1, 0, 0]] %188 := [[4, 2, 3, 5, 1], [0, 0, 1, 0]] %189 := [[1, 5, 3, 4, 2], [1, 1, 1, 1]] %190 := [[4, 2, 3, 1, 5], [1, 1, 1, 1]] %191 := [[1, 5, 3, 4, 2], [0, 1, 1, 1]] %192 := [[4, 2, 3, 1, 5], [1, 1, 1, 0]] %193 := [[1, 5, 3, 4, 2], [1, 0, 1, 1]] %194 := [[4, 2, 3, 1, 5], [1, 1, 0, 1]] %195 := [[1, 5, 3, 4, 2], [0, 0, 1, 1]] %196 := [[4, 2, 3, 1, 5], [1, 1, 0, 0]] %197 := [[1, 5, 3, 4, 2], [1, 1, 0, 1]] %198 := [[4, 2, 3, 1, 5], [1, 0, 1, 1]] %199 := [[1, 5, 3, 4, 2], [0, 1, 0, 1]] %200 := [[4, 2, 3, 1, 5], [1, 0, 1, 0]] %201 := [[1, 5, 3, 4, 2], [1, 1, 1, 0]] %202 := [[4, 2, 3, 1, 5], [0, 1, 1, 1]] %203 := [[1, 5, 3, 4, 2], [0, 1, 1, 0]] %204 := [[4, 2, 3, 1, 5], [0, 1, 1, 0]] %205 := [[1, 5, 3, 4, 2], [1, 0, 1, 0]] %206 := [[4, 2, 3, 1, 5], [0, 1, 0, 1]] %207 := [[1, 5, 3, 4, 2], [0, 0, 1, 0]] %208 := [[4, 2, 3, 1, 5], [0, 1, 0, 0]] %209 := [[1, 5, 3, 4, 2], [0, 1, 0, 0]] %210 := [[4, 2, 3, 1, 5], [0, 0, 1, 0]] %211 := [[1, 3, 5, 4, 2], [0, 1, 1, 1]] %212 := [[4, 2, 1, 3, 5], [1, 1, 1, 0]] %213 := [[1, 3, 5, 4, 2], [0, 0, 1, 1]] %214 := [[4, 2, 1, 3, 5], [1, 1, 0, 0]] %215 := [[1, 3, 5, 4, 2], [0, 1, 0, 1]] %216 := [[4, 2, 1, 3, 5], [1, 0, 1, 0]] %217 := [[1, 3, 5, 4, 2], [0, 1, 1, 0]] %218 := [[4, 2, 1, 3, 5], [0, 1, 1, 0]] %219 := [[1, 3, 5, 4, 2], [1, 0, 1, 0]] %220 := [[4, 2, 1, 3, 5], [0, 1, 0, 1]] %221 := [[1, 3, 5, 4, 2], [0, 0, 1, 0]] %222 := [[4, 2, 1, 3, 5], [0, 1, 0, 0]] %223 := [[1, 3, 5, 4, 2], [0, 1, 0, 0]] %224 := [[4, 2, 1, 3, 5], [0, 0, 1, 0]] %225 := [[1, 3, 4, 5, 2], [0, 1, 1, 1]] %226 := [[4, 1, 2, 3, 5], [1, 1, 1, 0]] %227 := [[1, 3, 4, 5, 2], [1, 0, 1, 1]] %228 := [[4, 1, 2, 3, 5], [1, 1, 0, 1]] %229 := [[1, 3, 4, 5, 2], [0, 0, 1, 1]] %230 := [[4, 1, 2, 3, 5], [1, 1, 0, 0]] %231 := [[1, 3, 4, 5, 2], [0, 1, 0, 1]] %232 := [[4, 1, 2, 3, 5], [1, 0, 1, 0]] %233 := [[1, 3, 4, 5, 2], [1, 1, 1, 0]] %234 := [[4, 1, 2, 3, 5], [0, 1, 1, 1]] %235 := [[1, 3, 4, 5, 2], [0, 1, 1, 0]] %236 := [[4, 1, 2, 3, 5], [0, 1, 1, 0]] %237 := [[1, 3, 4, 5, 2], [1, 0, 1, 0]] %238 := [[4, 1, 2, 3, 5], [0, 1, 0, 1]] %239 := [[1, 3, 4, 5, 2], [0, 0, 1, 0]] %240 := [[4, 1, 2, 3, 5], [0, 1, 0, 0]] %241 := [[1, 3, 4, 5, 2], [0, 1, 0, 0]] %242 := [[4, 1, 2, 3, 5], [0, 0, 1, 0]] %243 := [[5, 1, 4, 2, 3], [1, 0, 1, 1]] %244 := [[3, 4, 2, 5, 1], [1, 1, 0, 1]] %245 := [[5, 1, 4, 2, 3], [0, 0, 1, 1]] %246 := [[3, 4, 2, 5, 1], [1, 1, 0, 0]] %247 := [[5, 1, 4, 2, 3], [1, 0, 1, 0]] %248 := [[3, 4, 2, 5, 1], [0, 1, 0, 1]] %249 := [[5, 1, 4, 2, 3], [0, 0, 1, 0]] %250 := [[3, 4, 2, 5, 1], [0, 1, 0, 0]] %251 := [[1, 5, 4, 2, 3], [0, 1, 1, 1]] %252 := [[3, 4, 2, 1, 5], [1, 1, 1, 0]] %253 := [[1, 5, 4, 2, 3], [0, 0, 1, 1]] %254 := [[3, 4, 2, 1, 5], [1, 1, 0, 0]] %255 := [[1, 5, 4, 2, 3], [0, 1, 0, 1]] %256 := [[3, 4, 2, 1, 5], [1, 0, 1, 0]] %257 := [[1, 5, 4, 2, 3], [0, 1, 1, 0]] %258 := [[3, 4, 2, 1, 5], [0, 1, 1, 0]] %259 := [[1, 5, 4, 2, 3], [0, 0, 1, 0]] %260 := [[3, 4, 2, 1, 5], [0, 1, 0, 0]] %261 := [[1, 5, 4, 2, 3], [0, 1, 0, 0]] %262 := [[3, 4, 2, 1, 5], [0, 0, 1, 0]] %263 := [[1, 4, 5, 2, 3], [0, 1, 1, 1]] %264 := [[3, 4, 1, 2, 5], [1, 1, 1, 0]] %265 := [[1, 4, 5, 2, 3], [0, 0, 1, 1]] %266 := [[3, 4, 1, 2, 5], [1, 1, 0, 0]] %267 := [[1, 4, 5, 2, 3], [0, 1, 0, 1]] %268 := [[3, 4, 1, 2, 5], [1, 0, 1, 0]] %269 := [[1, 4, 5, 2, 3], [0, 1, 1, 0]] %270 := [[3, 4, 1, 2, 5], [0, 1, 1, 0]] %271 := [[1, 4, 5, 2, 3], [0, 0, 1, 0]] %272 := [[3, 4, 1, 2, 5], [0, 1, 0, 0]] %273 := [[1, 4, 5, 2, 3], [0, 1, 0, 0]] %274 := [[3, 4, 1, 2, 5], [0, 0, 1, 0]] %275 := [[5, 1, 2, 4, 3], [0, 1, 1, 1]] %276 := [[3, 2, 4, 5, 1], [1, 1, 1, 0]] %277 := [[5, 1, 2, 4, 3], [1, 1, 0, 1]] %278 := [[3, 2, 4, 5, 1], [1, 0, 1, 1]] %279 := [[5, 1, 2, 4, 3], [0, 1, 0, 1]] %280 := [[3, 2, 4, 5, 1], [1, 0, 1, 0]] %281 := [[5, 1, 2, 4, 3], [1, 1, 1, 0]] %282 := [[3, 2, 4, 5, 1], [0, 1, 1, 1]] %283 := [[5, 1, 2, 4, 3], [0, 1, 1, 0]] %284 := [[3, 2, 4, 5, 1], [0, 1, 1, 0]] %285 := [[5, 1, 2, 4, 3], [1, 1, 0, 0]] %286 := [[3, 2, 4, 5, 1], [0, 0, 1, 1]] %287 := [[5, 1, 2, 4, 3], [0, 1, 0, 0]] %288 := [[3, 2, 4, 5, 1], [0, 0, 1, 0]] %289 := [[1, 5, 2, 4, 3], [0, 1, 1, 1]] %290 := [[3, 2, 4, 1, 5], [1, 1, 1, 0]] %291 := [[1, 5, 2, 4, 3], [1, 1, 0, 1]] %292 := [[3, 2, 4, 1, 5], [1, 0, 1, 1]] %293 := [[1, 5, 2, 4, 3], [0, 1, 0, 1]] %294 := [[3, 2, 4, 1, 5], [1, 0, 1, 0]] %295 := [[1, 5, 2, 4, 3], [0, 1, 1, 0]] %296 := [[3, 2, 4, 1, 5], [0, 1, 1, 0]] %297 := [[1, 5, 2, 4, 3], [0, 1, 0, 0]] %298 := [[3, 2, 4, 1, 5], [0, 0, 1, 0]] %299 := [[1, 2, 5, 4, 3], [1, 0, 1, 1]] %300 := [[3, 2, 1, 4, 5], [1, 1, 0, 1]] %301 := [[1, 2, 5, 4, 3], [0, 0, 1, 1]] %302 := [[3, 2, 1, 4, 5], [1, 1, 0, 0]] %303 := [[1, 2, 5, 4, 3], [1, 0, 1, 0]] %304 := [[3, 2, 1, 4, 5], [0, 1, 0, 1]] %305 := [[1, 2, 5, 4, 3], [0, 0, 1, 0]] %306 := [[3, 2, 1, 4, 5], [0, 1, 0, 0]] %307 := [[1, 2, 4, 5, 3], [0, 1, 1, 1]] %308 := [[3, 1, 2, 4, 5], [1, 1, 1, 0]] %309 := [[1, 2, 4, 5, 3], [1, 0, 1, 1]] %310 := [[3, 1, 2, 4, 5], [1, 1, 0, 1]] %311 := [[1, 2, 4, 5, 3], [0, 0, 1, 1]] %312 := [[3, 1, 2, 4, 5], [1, 1, 0, 0]] %313 := [[1, 2, 4, 5, 3], [0, 1, 0, 1]] %314 := [[3, 1, 2, 4, 5], [1, 0, 1, 0]] %315 := [[1, 2, 4, 5, 3], [1, 1, 1, 0]] %316 := [[3, 1, 2, 4, 5], [0, 1, 1, 1]] %317 := [[1, 2, 4, 5, 3], [0, 1, 1, 0]] %318 := [[3, 1, 2, 4, 5], [0, 1, 1, 0]] %319 := [[1, 2, 4, 5, 3], [1, 0, 1, 0]] %320 := [[3, 1, 2, 4, 5], [0, 1, 0, 1]] %321 := [[1, 2, 4, 5, 3], [0, 0, 1, 0]] %322 := [[3, 1, 2, 4, 5], [0, 1, 0, 0]] %323 := [[1, 2, 4, 5, 3], [0, 1, 0, 0]] %324 := [[3, 1, 2, 4, 5], [0, 0, 1, 0]] %325 := [[5, 1, 2, 3, 4], [1, 1, 0, 1]] %326 := [[2, 3, 4, 5, 1], [1, 0, 1, 1]] %327 := [[5, 1, 2, 3, 4], [1, 1, 1, 0]] %328 := [[2, 3, 4, 5, 1], [0, 1, 1, 1]] %329 := [[5, 1, 2, 3, 4], [1, 1, 0, 0]] %330 := [[2, 3, 4, 5, 1], [0, 0, 1, 1]] %331 := [[1, 5, 2, 3, 4], [0, 1, 1, 1]] %332 := [[2, 3, 4, 1, 5], [1, 1, 1, 0]] %333 := [[1, 5, 2, 3, 4], [0, 1, 0, 1]] %334 := [[2, 3, 4, 1, 5], [1, 0, 1, 0]] %335 := [[1, 5, 2, 3, 4], [0, 1, 1, 0]] %336 := [[2, 3, 4, 1, 5], [0, 1, 1, 0]] %337 := [[1, 5, 2, 3, 4], [0, 1, 0, 0]] %338 := [[2, 3, 4, 1, 5], [0, 0, 1, 0]] %339 := [[1, 2, 5, 3, 4], [0, 0, 1, 1]] %340 := [[2, 3, 1, 4, 5], [1, 1, 0, 0]] %341 := [[1, 2, 5, 3, 4], [1, 0, 1, 0]] %342 := [[2, 3, 1, 4, 5], [0, 1, 0, 1]] %343 := [[1, 2, 5, 3, 4], [0, 0, 1, 0]] %344 := [[2, 3, 1, 4, 5], [0, 1, 0, 0]] %345 := [[1, 2, 3, 5, 4], [0, 1, 1, 1]] %346 := [[2, 1, 3, 4, 5], [1, 1, 1, 0]] %347 := [[1, 2, 3, 5, 4], [0, 1, 0, 1]] %348 := [[2, 1, 3, 4, 5], [1, 0, 1, 0]] %349 := [[1, 2, 3, 5, 4], [0, 1, 1, 0]] %350 := [[2, 1, 3, 4, 5], [0, 1, 1, 0]] %351 := [[1, 2, 3, 4, 5], [0, 1, 1, 1]] %352 := [[1, 2, 3, 4, 5], [1, 1, 1, 0]] %353 := [[1, 2, 3, 4, 5], [0, 1, 0, 1]] %354 := [[1, 2, 3, 4, 5], [1, 0, 1, 0]] %355 := [[1, 2, 3, 4, 5], [0, 1, 1, 0]] %356 := [[1, 2, 3, 4, 5], [0, 1, 0, 0]] %357 := [[1, 2, 3, 4, 5], [0, 0, 1, 0]] %358 := [[5, 4, 3, 2, 1], [0, 1, 1, 1]] %359 := [[2, 1, 3], [0, 1]] %360 := [[5, 4, 3, 2, 1], [1, 1, 1, 0]] %361 := [[1, 3, 2], [1, 0]] %362 := [[5, 4, 3, 2, 1], [1, 0, 1, 1]] %363 := [[5, 4, 3, 2, 1], [1, 1, 0, 1]] %364 := [[5, 4, 3, 2, 1], [0, 0, 1, 1]] %365 := [[5, 4, 3, 2, 1], [1, 1, 0, 0]] %366 := [[5, 4, 3, 2, 1], [0, 1, 1, 0]] %367 := [[4, 5, 3, 2, 1], [1, 1, 1, 1]] %368 := [[5, 4, 3, 1, 2], [1, 1, 1, 1]] %369 := [[4, 5, 3, 2, 1], [0, 1, 1, 1]] %370 := [[5, 4, 3, 1, 2], [1, 1, 1, 0]] %371 := [[4, 5, 3, 2, 1], [1, 0, 1, 1]] %372 := [[5, 4, 3, 1, 2], [1, 1, 0, 1]] %373 := [[4, 5, 3, 2, 1], [0, 0, 1, 1]] %374 := [[5, 4, 3, 1, 2], [1, 1, 0, 0]] %375 := [[4, 5, 3, 2, 1], [1, 1, 1, 0]] %376 := [[5, 4, 3, 1, 2], [0, 1, 1, 1]] %377 := [[4, 5, 3, 2, 1], [0, 1, 1, 0]] %378 := [[5, 4, 3, 1, 2], [0, 1, 1, 0]] %379 := [[5, 3, 4, 2, 1], [1, 1, 0, 1]] %380 := [[5, 4, 2, 3, 1], [1, 0, 1, 1]] %381 := [[5, 3, 4, 2, 1], [0, 1, 0, 1]] %382 := [[5, 4, 2, 3, 1], [1, 0, 1, 0]] %383 := [[5, 3, 4, 2, 1], [1, 1, 0, 0]] %384 := [[5, 4, 2, 3, 1], [0, 0, 1, 1]] %385 := [[5, 3, 4, 2, 1], [0, 1, 0, 0]] %386 := [[5, 4, 2, 3, 1], [0, 0, 1, 0]] %387 := [[3, 5, 4, 2, 1], [1, 1, 1, 1]] %388 := [[5, 4, 2, 1, 3], [1, 1, 1, 1]] %389 := [[3, 5, 4, 2, 1], [1, 0, 1, 1]] %390 := [[5, 4, 2, 1, 3], [1, 1, 0, 1]] %391 := [[3, 5, 4, 2, 1], [1, 1, 1, 0]] %392 := [[5, 4, 2, 1, 3], [0, 1, 1, 1]] %393 := [[4, 3, 5, 2, 1], [1, 1, 1, 1]] %394 := [[5, 4, 1, 3, 2], [1, 1, 1, 1]] %395 := [[4, 3, 5, 2, 1], [1, 1, 0, 1]] %396 := [[5, 4, 1, 3, 2], [1, 0, 1, 1]] %397 := [[4, 3, 5, 2, 1], [1, 1, 0, 0]] %398 := [[5, 4, 1, 3, 2], [0, 0, 1, 1]] %399 := [[3, 4, 5, 2, 1], [1, 1, 1, 1]] %400 := [[5, 4, 1, 2, 3], [1, 1, 1, 1]] %401 := [[3, 4, 5, 2, 1], [1, 1, 0, 1]] %402 := [[5, 4, 1, 2, 3], [1, 0, 1, 1]] %403 := [[3, 4, 5, 2, 1], [1, 1, 0, 0]] %404 := [[5, 4, 1, 2, 3], [0, 0, 1, 1]] %405 := [[5, 4, 2, 3, 1], [0, 1, 1, 1]] %406 := [[5, 3, 4, 2, 1], [1, 1, 1, 0]] %407 := [[5, 4, 2, 3, 1], [1, 1, 1, 0]] %408 := [[5, 3, 4, 2, 1], [0, 1, 1, 1]] %409 := [[5, 4, 2, 3, 1], [0, 1, 1, 0]] %410 := [[5, 3, 4, 2, 1], [0, 1, 1, 0]] %411 := [[4, 5, 2, 3, 1], [1, 1, 1, 1]] %412 := [[5, 3, 4, 1, 2], [1, 1, 1, 1]] %413 := [[4, 5, 2, 3, 1], [0, 1, 1, 1]] %414 := [[5, 3, 4, 1, 2], [1, 1, 1, 0]] %415 := [[4, 5, 2, 3, 1], [1, 1, 1, 0]] %416 := [[5, 3, 4, 1, 2], [0, 1, 1, 1]] %417 := [[4, 5, 2, 3, 1], [0, 1, 1, 0]] %418 := [[5, 3, 4, 1, 2], [0, 1, 1, 0]] %419 := [[5, 2, 4, 3, 1], [1, 1, 1, 1]] %420 := [[5, 3, 2, 4, 1], [1, 1, 1, 1]] %421 := [[5, 2, 4, 3, 1], [0, 1, 1, 1]] %422 := [[5, 3, 2, 4, 1], [1, 1, 1, 0]] %423 := [[5, 2, 4, 3, 1], [1, 1, 0, 1]] %424 := [[5, 3, 2, 4, 1], [1, 0, 1, 1]] %425 := [[5, 2, 4, 3, 1], [0, 1, 0, 1]] %426 := [[5, 3, 2, 4, 1], [1, 0, 1, 0]] %427 := [[5, 2, 4, 3, 1], [1, 1, 1, 0]] %428 := [[5, 3, 2, 4, 1], [0, 1, 1, 1]] %429 := [[5, 2, 4, 3, 1], [0, 1, 1, 0]] %430 := [[5, 3, 2, 4, 1], [0, 1, 1, 0]] %431 := [[2, 5, 4, 3, 1], [1, 1, 1, 1]] %432 := [[5, 3, 2, 1, 4], [1, 1, 1, 1]] %433 := [[2, 5, 4, 3, 1], [1, 0, 1, 1]] %434 := [[5, 3, 2, 1, 4], [1, 1, 0, 1]] %435 := [[2, 5, 4, 3, 1], [1, 1, 1, 0]] %436 := [[5, 3, 2, 1, 4], [0, 1, 1, 1]] %437 := [[2, 5, 4, 3, 1], [1, 0, 1, 0]] %438 := [[5, 3, 2, 1, 4], [0, 1, 0, 1]] %439 := [[4, 2, 5, 3, 1], [1, 1, 1, 1]] %440 := [[5, 3, 1, 4, 2], [1, 1, 1, 1]] %441 := [[4, 2, 5, 3, 1], [1, 0, 1, 1]] %442 := [[5, 3, 1, 4, 2], [1, 1, 0, 1]] %443 := [[4, 2, 5, 3, 1], [1, 1, 0, 1]] %444 := [[5, 3, 1, 4, 2], [1, 0, 1, 1]] %445 := [[4, 2, 5, 3, 1], [1, 1, 1, 0]] %446 := [[5, 3, 1, 4, 2], [0, 1, 1, 1]] %447 := [[4, 2, 5, 3, 1], [1, 0, 1, 0]] %448 := [[5, 3, 1, 4, 2], [0, 1, 0, 1]] %449 := [[4, 2, 5, 3, 1], [1, 1, 0, 0]] %450 := [[5, 3, 1, 4, 2], [0, 0, 1, 1]] %451 := [[2, 4, 5, 3, 1], [1, 1, 1, 1]] %452 := [[5, 3, 1, 2, 4], [1, 1, 1, 1]] %453 := [[2, 4, 5, 3, 1], [1, 0, 1, 1]] %454 := [[5, 3, 1, 2, 4], [1, 1, 0, 1]] %455 := [[2, 4, 5, 3, 1], [1, 1, 0, 1]] %456 := [[5, 3, 1, 2, 4], [1, 0, 1, 1]] %457 := [[2, 4, 5, 3, 1], [1, 1, 1, 0]] %458 := [[5, 3, 1, 2, 4], [0, 1, 1, 1]] %459 := [[2, 4, 5, 3, 1], [1, 1, 0, 0]] %460 := [[5, 3, 1, 2, 4], [0, 0, 1, 1]] %461 := [[3, 5, 2, 4, 1], [1, 1, 1, 1]] %462 := [[5, 2, 4, 1, 3], [1, 1, 1, 1]] %463 := [[3, 5, 2, 4, 1], [0, 1, 1, 1]] %464 := [[5, 2, 4, 1, 3], [1, 1, 1, 0]] %465 := [[3, 5, 2, 4, 1], [1, 1, 0, 1]] %466 := [[5, 2, 4, 1, 3], [1, 0, 1, 1]] %467 := [[3, 5, 2, 4, 1], [0, 1, 0, 1]] %468 := [[5, 2, 4, 1, 3], [1, 0, 1, 0]] %469 := [[3, 5, 2, 4, 1], [1, 1, 1, 0]] %470 := [[5, 2, 4, 1, 3], [0, 1, 1, 1]] %471 := [[3, 5, 2, 4, 1], [0, 1, 1, 0]] %472 := [[5, 2, 4, 1, 3], [0, 1, 1, 0]] %473 := [[3, 5, 2, 4, 1], [1, 0, 1, 0]] %474 := [[5, 2, 4, 1, 3], [0, 1, 0, 1]] %475 := [[3, 5, 2, 4, 1], [0, 0, 1, 0]] %476 := [[5, 2, 4, 1, 3], [0, 1, 0, 0]] %477 := [[3, 5, 2, 4, 1], [0, 1, 0, 0]] %478 := [[5, 2, 4, 1, 3], [0, 0, 1, 0]] %479 := [[5, 2, 3, 4, 1], [1, 1, 1, 1]] %480 := [[5, 2, 3, 4, 1], [1, 1, 0, 1]] %481 := [[5, 2, 3, 4, 1], [1, 0, 1, 1]] %482 := [[2, 5, 3, 4, 1], [1, 1, 1, 1]] %483 := [[5, 2, 3, 1, 4], [1, 1, 1, 1]] %484 := [[2, 5, 3, 4, 1], [1, 1, 0, 1]] %485 := [[5, 2, 3, 1, 4], [1, 0, 1, 1]] %486 := [[3, 2, 5, 4, 1], [1, 1, 1, 1]] %487 := [[5, 2, 1, 4, 3], [1, 1, 1, 1]] %488 := [[3, 2, 5, 4, 1], [1, 0, 1, 1]] %489 := [[5, 2, 1, 4, 3], [1, 1, 0, 1]] %490 := [[3, 2, 5, 4, 1], [1, 1, 0, 1]] %491 := [[5, 2, 1, 4, 3], [1, 0, 1, 1]] %492 := [[3, 2, 5, 4, 1], [1, 1, 1, 0]] %493 := [[5, 2, 1, 4, 3], [0, 1, 1, 1]] %494 := [[3, 2, 5, 4, 1], [1, 0, 1, 0]] %495 := [[5, 2, 1, 4, 3], [0, 1, 0, 1]] %496 := [[3, 2, 5, 4, 1], [1, 1, 0, 0]] %497 := [[5, 2, 1, 4, 3], [0, 0, 1, 1]] %498 := [[2, 3, 5, 4, 1], [1, 1, 1, 1]] %499 := [[5, 2, 1, 3, 4], [1, 1, 1, 1]] %500 := [[2, 3, 5, 4, 1], [0, 1, 1, 1]] %501 := [[5, 2, 1, 3, 4], [1, 1, 1, 0]] %502 := [[2, 3, 5, 4, 1], [1, 1, 0, 1]] %503 := [[5, 2, 1, 3, 4], [1, 0, 1, 1]] %504 := [[2, 3, 5, 4, 1], [0, 1, 0, 1]] %505 := [[5, 2, 1, 3, 4], [1, 0, 1, 0]] %506 := [[2, 3, 5, 4, 1], [1, 1, 1, 0]] %507 := [[5, 2, 1, 3, 4], [0, 1, 1, 1]] %508 := [[2, 3, 5, 4, 1], [1, 1, 0, 0]] %509 := [[5, 2, 1, 3, 4], [0, 0, 1, 1]] %510 := [[4, 3, 2, 5, 1], [1, 1, 1, 1]] %511 := [[5, 1, 4, 3, 2], [1, 1, 1, 1]] %512 := [[4, 3, 2, 5, 1], [1, 1, 1, 0]] %513 := [[5, 1, 4, 3, 2], [0, 1, 1, 1]] %514 := [[3, 4, 2, 5, 1], [1, 1, 1, 1]] %515 := [[5, 1, 4, 2, 3], [1, 1, 1, 1]] %516 := [[3, 4, 2, 5, 1], [0, 1, 1, 1]] %517 := [[5, 1, 4, 2, 3], [1, 1, 1, 0]] %518 := [[3, 4, 2, 5, 1], [1, 1, 1, 0]] %519 := [[5, 1, 4, 2, 3], [0, 1, 1, 1]] %520 := [[3, 4, 2, 5, 1], [0, 1, 1, 0]] %521 := [[5, 1, 4, 2, 3], [0, 1, 1, 0]] %522 := [[4, 2, 3, 5, 1], [1, 1, 1, 1]] %523 := [[5, 1, 3, 4, 2], [1, 1, 1, 1]] %524 := [[2, 4, 3, 5, 1], [1, 1, 1, 1]] %525 := [[5, 1, 3, 2, 4], [1, 1, 1, 1]] %526 := [[2, 4, 3, 5, 1], [0, 1, 1, 1]] %527 := [[5, 1, 3, 2, 4], [1, 1, 1, 0]] %528 := [[2, 4, 3, 5, 1], [1, 1, 0, 1]] %529 := [[5, 1, 3, 2, 4], [1, 0, 1, 1]] %530 := [[2, 4, 3, 5, 1], [0, 1, 0, 1]] %531 := [[5, 1, 3, 2, 4], [1, 0, 1, 0]] %532 := [[2, 4, 3, 5, 1], [1, 1, 1, 0]] %533 := [[5, 1, 3, 2, 4], [0, 1, 1, 1]] %534 := [[2, 4, 3, 5, 1], [0, 1, 1, 0]] %535 := [[5, 1, 3, 2, 4], [0, 1, 1, 0]] %536 := [[2, 4, 3, 5, 1], [1, 1, 0, 0]] %537 := [[5, 1, 3, 2, 4], [0, 0, 1, 1]] %538 := [[2, 4, 3, 5, 1], [0, 1, 0, 0]] %539 := [[5, 1, 3, 2, 4], [0, 0, 1, 0]] %540 := [[3, 2, 4, 5, 1], [1, 1, 1, 1]] %541 := [[5, 1, 2, 4, 3], [1, 1, 1, 1]] %542 := [[3, 2, 4, 5, 1], [1, 1, 0, 1]] %543 := [[5, 1, 2, 4, 3], [1, 0, 1, 1]] %544 := [[3, 2, 4, 5, 1], [1, 1, 0, 0]] %545 := [[5, 1, 2, 4, 3], [0, 0, 1, 1]] %546 := [[2, 3, 4, 5, 1], [1, 1, 1, 1]] %547 := [[5, 1, 2, 3, 4], [1, 1, 1, 1]] %548 := [[2, 3, 4, 5, 1], [1, 1, 0, 1]] %549 := [[5, 1, 2, 3, 4], [1, 0, 1, 1]] %550 := [[2, 3, 4, 5, 1], [0, 1, 0, 1]] %551 := [[5, 1, 2, 3, 4], [1, 0, 1, 0]] %552 := [[2, 3, 4, 5, 1], [1, 1, 0, 0]] %553 := [[5, 1, 2, 3, 4], [0, 0, 1, 1]] %554 := [[5, 4, 3, 1, 2], [0, 0, 1, 1]] %555 := [[4, 5, 3, 2, 1], [1, 1, 0, 0]] %556 := [[4, 5, 3, 1, 2], [1, 1, 1, 1]] %557 := [[4, 5, 3, 1, 2], [0, 1, 1, 1]] %558 := [[4, 5, 3, 1, 2], [1, 1, 1, 0]] %559 := [[4, 5, 3, 1, 2], [1, 0, 1, 1]] %560 := [[4, 5, 3, 1, 2], [1, 1, 0, 1]] %561 := [[4, 5, 3, 1, 2], [0, 0, 1, 1]] %562 := [[4, 5, 3, 1, 2], [1, 1, 0, 0]] %563 := [[4, 5, 3, 1, 2], [0, 1, 1, 0]] %564 := [[3, 5, 4, 1, 2], [1, 0, 1, 1]] %565 := [[4, 5, 2, 1, 3], [1, 1, 0, 1]] %566 := [[3, 5, 4, 1, 2], [1, 1, 0, 1]] %567 := [[4, 5, 2, 1, 3], [1, 0, 1, 1]] %568 := [[3, 5, 4, 1, 2], [1, 0, 0, 1]] %569 := [[4, 5, 2, 1, 3], [1, 0, 0, 1]] %570 := [[3, 5, 4, 1, 2], [1, 1, 1, 0]] %571 := [[4, 5, 2, 1, 3], [0, 1, 1, 1]] %572 := [[3, 5, 4, 1, 2], [1, 1, 0, 0]] %573 := [[4, 5, 2, 1, 3], [0, 0, 1, 1]] %574 := [[4, 3, 5, 1, 2], [1, 1, 0, 1]] %575 := [[4, 5, 1, 3, 2], [1, 0, 1, 1]] %576 := [[4, 3, 5, 1, 2], [1, 1, 1, 0]] %577 := [[4, 5, 1, 3, 2], [0, 1, 1, 1]] %578 := [[4, 3, 5, 1, 2], [1, 1, 0, 0]] %579 := [[4, 5, 1, 3, 2], [0, 0, 1, 1]] %580 := [[3, 4, 5, 1, 2], [1, 1, 1, 1]] %581 := [[4, 5, 1, 2, 3], [1, 1, 1, 1]] %582 := [[3, 4, 5, 1, 2], [1, 0, 1, 1]] %583 := [[4, 5, 1, 2, 3], [1, 1, 0, 1]] %584 := [[3, 4, 5, 1, 2], [1, 1, 0, 1]] %585 := [[4, 5, 1, 2, 3], [1, 0, 1, 1]] %586 := [[3, 4, 5, 1, 2], [1, 0, 0, 1]] %587 := [[4, 5, 1, 2, 3], [1, 0, 0, 1]] %588 := [[3, 4, 5, 1, 2], [1, 1, 1, 0]] %589 := [[4, 5, 1, 2, 3], [0, 1, 1, 1]] %590 := [[3, 4, 5, 1, 2], [1, 1, 0, 0]] %591 := [[4, 5, 1, 2, 3], [0, 0, 1, 1]] %592 := [[5, 4, 1, 3, 2], [0, 1, 1, 1]] %593 := [[4, 3, 5, 2, 1], [1, 1, 1, 0]] %594 := [[5, 4, 1, 3, 2], [0, 1, 1, 0]] %595 := [[4, 3, 5, 2, 1], [0, 1, 1, 0]] %596 := [[4, 5, 1, 3, 2], [1, 1, 1, 0]] %597 := [[4, 3, 5, 1, 2], [0, 1, 1, 1]] %598 := [[4, 5, 1, 3, 2], [0, 1, 1, 0]] %599 := [[4, 3, 5, 1, 2], [0, 1, 1, 0]] %600 := [[4, 5, 1, 3, 2], [1, 0, 1, 0]] %601 := [[4, 3, 5, 1, 2], [0, 1, 0, 1]] %602 := [[4, 5, 1, 3, 2], [0, 0, 1, 0]] %603 := [[4, 3, 5, 1, 2], [0, 1, 0, 0]] %604 := [[5, 1, 4, 3, 2], [1, 1, 1, 0]] %605 := [[4, 3, 2, 5, 1], [0, 1, 1, 1]] %606 := [[5, 1, 4, 3, 2], [0, 1, 1, 0]] %607 := [[4, 3, 2, 5, 1], [0, 1, 1, 0]] %608 := [[1, 5, 4, 3, 2], [1, 1, 1, 1]] %609 := [[4, 3, 2, 1, 5], [1, 1, 1, 1]] %610 := [[1, 5, 4, 3, 2], [1, 0, 1, 1]] %611 := [[4, 3, 2, 1, 5], [1, 1, 0, 1]] %612 := [[1, 5, 4, 3, 2], [1, 1, 1, 0]] %613 := [[4, 3, 2, 1, 5], [0, 1, 1, 1]] %614 := [[1, 5, 4, 3, 2], [1, 0, 1, 0]] %615 := [[4, 3, 2, 1, 5], [0, 1, 0, 1]] %616 := [[4, 1, 5, 3, 2], [1, 1, 1, 1]] %617 := [[4, 3, 1, 5, 2], [1, 1, 1, 1]] %618 := [[4, 1, 5, 3, 2], [1, 0, 1, 1]] %619 := [[4, 3, 1, 5, 2], [1, 1, 0, 1]] %620 := [[4, 1, 5, 3, 2], [1, 1, 0, 1]] %621 := [[4, 3, 1, 5, 2], [1, 0, 1, 1]] %622 := [[4, 1, 5, 3, 2], [1, 0, 0, 1]] %623 := [[4, 3, 1, 5, 2], [1, 0, 0, 1]] %624 := [[4, 1, 5, 3, 2], [1, 1, 1, 0]] %625 := [[4, 3, 1, 5, 2], [0, 1, 1, 1]] %626 := [[4, 1, 5, 3, 2], [1, 0, 1, 0]] %627 := [[4, 3, 1, 5, 2], [0, 1, 0, 1]] %628 := [[4, 1, 5, 3, 2], [1, 1, 0, 0]] %629 := [[4, 3, 1, 5, 2], [0, 0, 1, 1]] %630 := [[1, 4, 5, 3, 2], [1, 1, 1, 1]] %631 := [[4, 3, 1, 2, 5], [1, 1, 1, 1]] %632 := [[1, 4, 5, 3, 2], [1, 0, 1, 1]] %633 := [[4, 3, 1, 2, 5], [1, 1, 0, 1]] %634 := [[1, 4, 5, 3, 2], [1, 1, 1, 0]] %635 := [[4, 3, 1, 2, 5], [0, 1, 1, 1]] %636 := [[1, 4, 5, 3, 2], [1, 1, 0, 0]] %637 := [[4, 3, 1, 2, 5], [0, 0, 1, 1]] %638 := [[5, 3, 1, 4, 2], [1, 1, 1, 0]] %639 := [[4, 2, 5, 3, 1], [0, 1, 1, 1]] %640 := [[5, 3, 1, 4, 2], [0, 1, 1, 0]] %641 := [[4, 2, 5, 3, 1], [0, 1, 1, 0]] %642 := [[5, 3, 1, 4, 2], [1, 1, 0, 0]] %643 := [[4, 2, 5, 3, 1], [0, 0, 1, 1]] %644 := [[5, 3, 1, 4, 2], [0, 1, 0, 0]] %645 := [[4, 2, 5, 3, 1], [0, 0, 1, 0]] %646 := [[3, 5, 1, 4, 2], [1, 1, 1, 1]] %647 := [[4, 2, 5, 1, 3], [1, 1, 1, 1]] %648 := [[3, 5, 1, 4, 2], [0, 1, 1, 1]] %649 := [[4, 2, 5, 1, 3], [1, 1, 1, 0]] %650 := [[3, 5, 1, 4, 2], [1, 0, 1, 1]] %651 := [[4, 2, 5, 1, 3], [1, 1, 0, 1]] %652 := [[3, 5, 1, 4, 2], [0, 0, 1, 1]] %653 := [[4, 2, 5, 1, 3], [1, 1, 0, 0]] %654 := [[3, 5, 1, 4, 2], [1, 1, 0, 1]] %655 := [[4, 2, 5, 1, 3], [1, 0, 1, 1]] %656 := [[3, 5, 1, 4, 2], [0, 1, 0, 1]] %657 := [[4, 2, 5, 1, 3], [1, 0, 1, 0]] %658 := [[3, 5, 1, 4, 2], [1, 0, 0, 1]] %659 := [[4, 2, 5, 1, 3], [1, 0, 0, 1]] %660 := [[3, 5, 1, 4, 2], [1, 1, 1, 0]] %661 := [[4, 2, 5, 1, 3], [0, 1, 1, 1]] %662 := [[3, 5, 1, 4, 2], [0, 1, 1, 0]] %663 := [[4, 2, 5, 1, 3], [0, 1, 1, 0]] %664 := [[3, 5, 1, 4, 2], [1, 0, 1, 0]] %665 := [[4, 2, 5, 1, 3], [0, 1, 0, 1]] %666 := [[3, 5, 1, 4, 2], [0, 0, 1, 0]] %667 := [[4, 2, 5, 1, 3], [0, 1, 0, 0]] %668 := [[3, 5, 1, 4, 2], [0, 1, 0, 0]] %669 := [[4, 2, 5, 1, 3], [0, 0, 1, 0]] %670 := [[3, 1, 5, 4, 2], [1, 1, 1, 1]] %671 := [[4, 2, 1, 5, 3], [1, 1, 1, 1]] %672 := [[3, 1, 5, 4, 2], [1, 0, 1, 1]] %673 := [[4, 2, 1, 5, 3], [1, 1, 0, 1]] %674 := [[3, 1, 5, 4, 2], [1, 1, 0, 1]] %675 := [[4, 2, 1, 5, 3], [1, 0, 1, 1]] %676 := [[3, 1, 5, 4, 2], [1, 0, 0, 1]] %677 := [[4, 2, 1, 5, 3], [1, 0, 0, 1]] %678 := [[3, 1, 5, 4, 2], [1, 1, 1, 0]] %679 := [[4, 2, 1, 5, 3], [0, 1, 1, 1]] %680 := [[3, 1, 5, 4, 2], [1, 0, 1, 0]] %681 := [[4, 2, 1, 5, 3], [0, 1, 0, 1]] %682 := [[3, 1, 5, 4, 2], [1, 1, 0, 0]] %683 := [[4, 2, 1, 5, 3], [0, 0, 1, 1]] %684 := [[1, 3, 5, 4, 2], [1, 1, 1, 1]] %685 := [[4, 2, 1, 3, 5], [1, 1, 1, 1]] %686 := [[1, 3, 5, 4, 2], [1, 0, 1, 1]] %687 := [[4, 2, 1, 3, 5], [1, 1, 0, 1]] %688 := [[1, 3, 5, 4, 2], [1, 1, 0, 1]] %689 := [[4, 2, 1, 3, 5], [1, 0, 1, 1]] %690 := [[1, 3, 5, 4, 2], [1, 1, 1, 0]] %691 := [[4, 2, 1, 3, 5], [0, 1, 1, 1]] %692 := [[1, 3, 5, 4, 2], [1, 1, 0, 0]] %693 := [[4, 2, 1, 3, 5], [0, 0, 1, 1]] %694 := [[4, 3, 1, 5, 2], [1, 1, 1, 0]] %695 := [[4, 1, 5, 3, 2], [0, 1, 1, 1]] %696 := [[4, 3, 1, 5, 2], [1, 1, 0, 0]] %697 := [[4, 1, 5, 3, 2], [0, 0, 1, 1]] %698 := [[3, 4, 1, 5, 2], [1, 1, 1, 1]] %699 := [[4, 1, 5, 2, 3], [1, 1, 1, 1]] %700 := [[3, 4, 1, 5, 2], [0, 1, 1, 1]] %701 := [[4, 1, 5, 2, 3], [1, 1, 1, 0]] %702 := [[3, 4, 1, 5, 2], [1, 1, 0, 1]] %703 := [[4, 1, 5, 2, 3], [1, 0, 1, 1]] %704 := [[3, 4, 1, 5, 2], [0, 1, 0, 1]] %705 := [[4, 1, 5, 2, 3], [1, 0, 1, 0]] %706 := [[3, 4, 1, 5, 2], [1, 1, 1, 0]] %707 := [[4, 1, 5, 2, 3], [0, 1, 1, 1]] %708 := [[3, 4, 1, 5, 2], [0, 1, 1, 0]] %709 := [[4, 1, 5, 2, 3], [0, 1, 1, 0]] %710 := [[3, 4, 1, 5, 2], [1, 1, 0, 0]] %711 := [[4, 1, 5, 2, 3], [0, 0, 1, 1]] %712 := [[3, 4, 1, 5, 2], [0, 1, 0, 0]] %713 := [[4, 1, 5, 2, 3], [0, 0, 1, 0]] %714 := [[4, 1, 3, 5, 2], [1, 1, 1, 1]] %715 := [[4, 1, 3, 5, 2], [1, 0, 1, 1]] %716 := [[4, 1, 3, 5, 2], [1, 1, 0, 1]] %717 := [[4, 1, 3, 5, 2], [1, 0, 0, 1]] %718 := [[4, 1, 3, 5, 2], [1, 1, 1, 0]] %719 := [[4, 1, 3, 5, 2], [0, 1, 1, 1]] %720 := [[4, 1, 3, 5, 2], [1, 0, 1, 0]] %721 := [[4, 1, 3, 5, 2], [0, 1, 0, 1]] %722 := [[4, 1, 3, 5, 2], [1, 1, 0, 0]] %723 := [[4, 1, 3, 5, 2], [0, 0, 1, 1]] %724 := [[1, 4, 3, 5, 2], [1, 1, 1, 1]] %725 := [[4, 1, 3, 2, 5], [1, 1, 1, 1]] %726 := [[1, 4, 3, 5, 2], [0, 1, 1, 1]] %727 := [[4, 1, 3, 2, 5], [1, 1, 1, 0]] %728 := [[1, 4, 3, 5, 2], [1, 1, 0, 1]] %729 := [[4, 1, 3, 2, 5], [1, 0, 1, 1]] %730 := [[1, 4, 3, 5, 2], [0, 1, 0, 1]] %731 := [[4, 1, 3, 2, 5], [1, 0, 1, 0]] %732 := [[1, 4, 3, 5, 2], [1, 1, 1, 0]] %733 := [[4, 1, 3, 2, 5], [0, 1, 1, 1]] %734 := [[1, 4, 3, 5, 2], [0, 1, 1, 0]] %735 := [[4, 1, 3, 2, 5], [0, 1, 1, 0]] %736 := [[1, 4, 3, 5, 2], [1, 1, 0, 0]] %737 := [[4, 1, 3, 2, 5], [0, 0, 1, 1]] %738 := [[1, 4, 3, 5, 2], [0, 1, 0, 0]] %739 := [[4, 1, 3, 2, 5], [0, 0, 1, 0]] %740 := [[3, 1, 4, 5, 2], [1, 1, 1, 1]] %741 := [[4, 1, 2, 5, 3], [1, 1, 1, 1]] %742 := [[3, 1, 4, 5, 2], [1, 0, 1, 1]] %743 := [[4, 1, 2, 5, 3], [1, 1, 0, 1]] %744 := [[3, 1, 4, 5, 2], [1, 1, 0, 1]] %745 := [[4, 1, 2, 5, 3], [1, 0, 1, 1]] %746 := [[3, 1, 4, 5, 2], [1, 0, 0, 1]] %747 := [[4, 1, 2, 5, 3], [1, 0, 0, 1]] %748 := [[3, 1, 4, 5, 2], [1, 1, 1, 0]] %749 := [[4, 1, 2, 5, 3], [0, 1, 1, 1]] %750 := [[3, 1, 4, 5, 2], [1, 0, 1, 0]] %751 := [[4, 1, 2, 5, 3], [0, 1, 0, 1]] %752 := [[3, 1, 4, 5, 2], [1, 1, 0, 0]] %753 := [[4, 1, 2, 5, 3], [0, 0, 1, 1]] %754 := [[1, 3, 4, 5, 2], [1, 1, 1, 1]] %755 := [[4, 1, 2, 3, 5], [1, 1, 1, 1]] %756 := [[1, 3, 4, 5, 2], [1, 1, 0, 1]] %757 := [[4, 1, 2, 3, 5], [1, 0, 1, 1]] %758 := [[1, 3, 4, 5, 2], [1, 1, 0, 0]] %759 := [[4, 1, 2, 3, 5], [0, 0, 1, 1]] %760 := [[5, 4, 2, 1, 3], [1, 0, 1, 1]] %761 := [[3, 5, 4, 2, 1], [1, 1, 0, 1]] %762 := [[5, 4, 2, 1, 3], [0, 0, 1, 1]] %763 := [[3, 5, 4, 2, 1], [1, 1, 0, 0]] %764 := [[5, 2, 4, 1, 3], [0, 0, 1, 1]] %765 := [[3, 5, 2, 4, 1], [1, 1, 0, 0]] %766 := [[5, 2, 4, 1, 3], [1, 1, 0, 1]] %767 := [[3, 5, 2, 4, 1], [1, 0, 1, 1]] %768 := [[5, 2, 4, 1, 3], [1, 1, 0, 0]] %769 := [[3, 5, 2, 4, 1], [0, 0, 1, 1]] %770 := [[2, 5, 4, 1, 3], [1, 1, 1, 1]] %771 := [[3, 5, 2, 1, 4], [1, 1, 1, 1]] %772 := [[2, 5, 4, 1, 3], [0, 1, 1, 1]] %773 := [[3, 5, 2, 1, 4], [1, 1, 1, 0]] %774 := [[2, 5, 4, 1, 3], [1, 0, 1, 1]] %775 := [[3, 5, 2, 1, 4], [1, 1, 0, 1]] %776 := [[2, 5, 4, 1, 3], [0, 0, 1, 1]] %777 := [[3, 5, 2, 1, 4], [1, 1, 0, 0]] %778 := [[2, 5, 4, 1, 3], [0, 1, 0, 1]] %779 := [[3, 5, 2, 1, 4], [1, 0, 1, 0]] %780 := [[2, 5, 4, 1, 3], [1, 1, 1, 0]] %781 := [[3, 5, 2, 1, 4], [0, 1, 1, 1]] %782 := [[2, 5, 4, 1, 3], [0, 1, 1, 0]] %783 := [[3, 5, 2, 1, 4], [0, 1, 1, 0]] %784 := [[2, 5, 4, 1, 3], [1, 0, 1, 0]] %785 := [[3, 5, 2, 1, 4], [0, 1, 0, 1]] %786 := [[2, 5, 4, 1, 3], [0, 0, 1, 0]] %787 := [[3, 5, 2, 1, 4], [0, 1, 0, 0]] %788 := [[2, 5, 4, 1, 3], [1, 1, 0, 0]] %789 := [[3, 5, 2, 1, 4], [0, 0, 1, 1]] %790 := [[2, 5, 4, 1, 3], [0, 1, 0, 0]] %791 := [[3, 5, 2, 1, 4], [0, 0, 1, 0]] %792 := [[2, 4, 5, 1, 3], [1, 1, 1, 1]] %793 := [[3, 5, 1, 2, 4], [1, 1, 1, 1]] %794 := [[2, 4, 5, 1, 3], [0, 1, 1, 1]] %795 := [[3, 5, 1, 2, 4], [1, 1, 1, 0]] %796 := [[2, 4, 5, 1, 3], [1, 0, 1, 1]] %797 := [[3, 5, 1, 2, 4], [1, 1, 0, 1]] %798 := [[2, 4, 5, 1, 3], [0, 0, 1, 1]] %799 := [[3, 5, 1, 2, 4], [1, 1, 0, 0]] %800 := [[2, 4, 5, 1, 3], [1, 1, 0, 1]] %801 := [[3, 5, 1, 2, 4], [1, 0, 1, 1]] %802 := [[2, 4, 5, 1, 3], [0, 1, 0, 1]] %803 := [[3, 5, 1, 2, 4], [1, 0, 1, 0]] %804 := [[2, 4, 5, 1, 3], [1, 0, 0, 1]] %805 := [[3, 5, 1, 2, 4], [1, 0, 0, 1]] %806 := [[2, 4, 5, 1, 3], [1, 1, 1, 0]] %807 := [[3, 5, 1, 2, 4], [0, 1, 1, 1]] %808 := [[2, 4, 5, 1, 3], [0, 1, 1, 0]] %809 := [[3, 5, 1, 2, 4], [0, 1, 1, 0]] %810 := [[2, 4, 5, 1, 3], [1, 0, 1, 0]] %811 := [[3, 5, 1, 2, 4], [0, 1, 0, 1]] %812 := [[2, 4, 5, 1, 3], [0, 0, 1, 0]] %813 := [[3, 5, 1, 2, 4], [0, 1, 0, 0]] %814 := [[2, 4, 5, 1, 3], [1, 1, 0, 0]] %815 := [[3, 5, 1, 2, 4], [0, 0, 1, 1]] %816 := [[2, 4, 5, 1, 3], [0, 1, 0, 0]] %817 := [[3, 5, 1, 2, 4], [0, 0, 1, 0]] %818 := [[5, 4, 1, 2, 3], [0, 1, 1, 1]] %819 := [[3, 4, 5, 2, 1], [1, 1, 1, 0]] %820 := [[5, 4, 1, 2, 3], [0, 1, 1, 0]] %821 := [[3, 4, 5, 2, 1], [0, 1, 1, 0]] %822 := [[4, 5, 1, 2, 3], [1, 1, 1, 0]] %823 := [[3, 4, 5, 1, 2], [0, 1, 1, 1]] %824 := [[4, 5, 1, 2, 3], [0, 1, 1, 0]] %825 := [[3, 4, 5, 1, 2], [0, 1, 1, 0]] %826 := [[1, 5, 4, 2, 3], [1, 1, 1, 1]] %827 := [[3, 4, 2, 1, 5], [1, 1, 1, 1]] %828 := [[1, 5, 4, 2, 3], [1, 0, 1, 1]] %829 := [[3, 4, 2, 1, 5], [1, 1, 0, 1]] %830 := [[1, 5, 4, 2, 3], [1, 1, 1, 0]] %831 := [[3, 4, 2, 1, 5], [0, 1, 1, 1]] %832 := [[1, 5, 4, 2, 3], [1, 0, 1, 0]] %833 := [[3, 4, 2, 1, 5], [0, 1, 0, 1]] %834 := [[4, 1, 5, 2, 3], [1, 1, 0, 1]] %835 := [[3, 4, 1, 5, 2], [1, 0, 1, 1]] %836 := [[4, 1, 5, 2, 3], [1, 0, 0, 1]] %837 := [[3, 4, 1, 5, 2], [1, 0, 0, 1]] %838 := [[4, 1, 5, 2, 3], [1, 1, 0, 0]] %839 := [[3, 4, 1, 5, 2], [0, 0, 1, 1]] %840 := [[1, 4, 5, 2, 3], [1, 1, 1, 1]] %841 := [[3, 4, 1, 2, 5], [1, 1, 1, 1]] %842 := [[1, 4, 5, 2, 3], [1, 0, 1, 1]] %843 := [[3, 4, 1, 2, 5], [1, 1, 0, 1]] %844 := [[1, 4, 5, 2, 3], [1, 1, 0, 1]] %845 := [[3, 4, 1, 2, 5], [1, 0, 1, 1]] %846 := [[1, 4, 5, 2, 3], [1, 1, 1, 0]] %847 := [[3, 4, 1, 2, 5], [0, 1, 1, 1]] %848 := [[1, 4, 5, 2, 3], [1, 0, 1, 0]] %849 := [[3, 4, 1, 2, 5], [0, 1, 0, 1]] %850 := [[1, 4, 5, 2, 3], [1, 1, 0, 0]] %851 := [[3, 4, 1, 2, 5], [0, 0, 1, 1]] %852 := [[5, 2, 1, 4, 3], [1, 1, 1, 0]] %853 := [[3, 2, 5, 4, 1], [0, 1, 1, 1]] %854 := [[5, 2, 1, 4, 3], [0, 1, 1, 0]] %855 := [[3, 2, 5, 4, 1], [0, 1, 1, 0]] %856 := [[5, 2, 1, 4, 3], [1, 1, 0, 0]] %857 := [[3, 2, 5, 4, 1], [0, 0, 1, 1]] %858 := [[5, 2, 1, 4, 3], [0, 1, 0, 0]] %859 := [[3, 2, 5, 4, 1], [0, 0, 1, 0]] %860 := [[2, 5, 1, 4, 3], [1, 1, 1, 1]] %861 := [[3, 2, 5, 1, 4], [1, 1, 1, 1]] %862 := [[2, 5, 1, 4, 3], [0, 1, 1, 1]] %863 := [[3, 2, 5, 1, 4], [1, 1, 1, 0]] %864 := [[2, 5, 1, 4, 3], [1, 0, 1, 1]] %865 := [[3, 2, 5, 1, 4], [1, 1, 0, 1]] %866 := [[2, 5, 1, 4, 3], [0, 0, 1, 1]] %867 := [[3, 2, 5, 1, 4], [1, 1, 0, 0]] %868 := [[2, 5, 1, 4, 3], [1, 1, 0, 1]] %869 := [[3, 2, 5, 1, 4], [1, 0, 1, 1]] %870 := [[2, 5, 1, 4, 3], [0, 1, 0, 1]] %871 := [[3, 2, 5, 1, 4], [1, 0, 1, 0]] %872 := [[2, 5, 1, 4, 3], [1, 0, 0, 1]] %873 := [[3, 2, 5, 1, 4], [1, 0, 0, 1]] %874 := [[2, 5, 1, 4, 3], [1, 1, 1, 0]] %875 := [[3, 2, 5, 1, 4], [0, 1, 1, 1]] %876 := [[2, 5, 1, 4, 3], [0, 1, 1, 0]] %877 := [[3, 2, 5, 1, 4], [0, 1, 1, 0]] %878 := [[2, 5, 1, 4, 3], [0, 1, 0, 0]] %879 := [[3, 2, 5, 1, 4], [0, 0, 1, 0]] %880 := [[5, 1, 2, 4, 3], [1, 0, 1, 0]] %881 := [[3, 2, 4, 5, 1], [0, 1, 0, 1]] %882 := [[1, 5, 2, 4, 3], [1, 1, 1, 0]] %883 := [[3, 2, 4, 1, 5], [0, 1, 1, 1]] %884 := [[2, 1, 5, 4, 3], [1, 1, 1, 1]] %885 := [[3, 2, 1, 5, 4], [1, 1, 1, 1]] %886 := [[2, 1, 5, 4, 3], [1, 0, 1, 1]] %887 := [[3, 2, 1, 5, 4], [1, 1, 0, 1]] %888 := [[2, 1, 5, 4, 3], [1, 1, 0, 1]] %889 := [[3, 2, 1, 5, 4], [1, 0, 1, 1]] %890 := [[2, 1, 5, 4, 3], [1, 0, 0, 1]] %891 := [[3, 2, 1, 5, 4], [1, 0, 0, 1]] %892 := [[2, 1, 5, 4, 3], [1, 1, 1, 0]] %893 := [[3, 2, 1, 5, 4], [0, 1, 1, 1]] %894 := [[2, 1, 5, 4, 3], [1, 0, 1, 0]] %895 := [[3, 2, 1, 5, 4], [0, 1, 0, 1]] %896 := [[2, 1, 5, 4, 3], [1, 1, 0, 0]] %897 := [[3, 2, 1, 5, 4], [0, 0, 1, 1]] %898 := [[1, 2, 5, 4, 3], [1, 1, 1, 1]] %899 := [[3, 2, 1, 4, 5], [1, 1, 1, 1]] %900 := [[1, 2, 5, 4, 3], [0, 1, 1, 1]] %901 := [[3, 2, 1, 4, 5], [1, 1, 1, 0]] %902 := [[1, 2, 5, 4, 3], [1, 1, 0, 1]] %903 := [[3, 2, 1, 4, 5], [1, 0, 1, 1]] %904 := [[1, 2, 5, 4, 3], [1, 1, 1, 0]] %905 := [[3, 2, 1, 4, 5], [0, 1, 1, 1]] %906 := [[1, 2, 5, 4, 3], [0, 1, 1, 0]] %907 := [[3, 2, 1, 4, 5], [0, 1, 1, 0]] %908 := [[1, 2, 5, 4, 3], [1, 1, 0, 0]] %909 := [[3, 2, 1, 4, 5], [0, 0, 1, 1]] %910 := [[4, 2, 1, 5, 3], [1, 1, 1, 0]] %911 := [[3, 1, 5, 4, 2], [0, 1, 1, 1]] %912 := [[4, 2, 1, 5, 3], [1, 1, 0, 0]] %913 := [[3, 1, 5, 4, 2], [0, 0, 1, 1]] %914 := [[2, 4, 1, 5, 3], [1, 1, 1, 1]] %915 := [[3, 1, 5, 2, 4], [1, 1, 1, 1]] %916 := [[2, 4, 1, 5, 3], [0, 1, 1, 1]] %917 := [[3, 1, 5, 2, 4], [1, 1, 1, 0]] %918 := [[2, 4, 1, 5, 3], [1, 1, 0, 1]] %919 := [[3, 1, 5, 2, 4], [1, 0, 1, 1]] %920 := [[2, 4, 1, 5, 3], [0, 1, 0, 1]] %921 := [[3, 1, 5, 2, 4], [1, 0, 1, 0]] %922 := [[2, 4, 1, 5, 3], [1, 1, 1, 0]] %923 := [[3, 1, 5, 2, 4], [0, 1, 1, 1]] %924 := [[2, 4, 1, 5, 3], [0, 1, 1, 0]] %925 := [[3, 1, 5, 2, 4], [0, 1, 1, 0]] %926 := [[2, 4, 1, 5, 3], [1, 1, 0, 0]] %927 := [[3, 1, 5, 2, 4], [0, 0, 1, 1]] %928 := [[2, 4, 1, 5, 3], [0, 1, 0, 0]] %929 := [[3, 1, 5, 2, 4], [0, 0, 1, 0]] %930 := [[4, 1, 2, 5, 3], [1, 1, 1, 0]] %931 := [[3, 1, 4, 5, 2], [0, 1, 1, 1]] %932 := [[4, 1, 2, 5, 3], [1, 0, 1, 0]] %933 := [[3, 1, 4, 5, 2], [0, 1, 0, 1]] %934 := [[4, 1, 2, 5, 3], [1, 1, 0, 0]] %935 := [[3, 1, 4, 5, 2], [0, 0, 1, 1]] %936 := [[1, 4, 2, 5, 3], [1, 1, 1, 1]] %937 := [[3, 1, 4, 2, 5], [1, 1, 1, 1]] %938 := [[1, 4, 2, 5, 3], [0, 1, 1, 1]] %939 := [[3, 1, 4, 2, 5], [1, 1, 1, 0]] %940 := [[1, 4, 2, 5, 3], [1, 1, 0, 1]] %941 := [[3, 1, 4, 2, 5], [1, 0, 1, 1]] %942 := [[1, 4, 2, 5, 3], [0, 1, 0, 1]] %943 := [[3, 1, 4, 2, 5], [1, 0, 1, 0]] %944 := [[1, 4, 2, 5, 3], [1, 1, 1, 0]] %945 := [[3, 1, 4, 2, 5], [0, 1, 1, 1]] %946 := [[1, 4, 2, 5, 3], [0, 1, 1, 0]] %947 := [[3, 1, 4, 2, 5], [0, 1, 1, 0]] %948 := [[1, 4, 2, 5, 3], [1, 1, 0, 0]] %949 := [[3, 1, 4, 2, 5], [0, 0, 1, 1]] %950 := [[2, 1, 4, 5, 3], [1, 1, 1, 1]] %951 := [[3, 1, 2, 5, 4], [1, 1, 1, 1]] %952 := [[2, 1, 4, 5, 3], [1, 0, 1, 1]] %953 := [[3, 1, 2, 5, 4], [1, 1, 0, 1]] %954 := [[2, 1, 4, 5, 3], [1, 1, 0, 1]] %955 := [[3, 1, 2, 5, 4], [1, 0, 1, 1]] %956 := [[2, 1, 4, 5, 3], [1, 0, 0, 1]] %957 := [[3, 1, 2, 5, 4], [1, 0, 0, 1]] %958 := [[2, 1, 4, 5, 3], [1, 1, 1, 0]] %959 := [[3, 1, 2, 5, 4], [0, 1, 1, 1]] %960 := [[2, 1, 4, 5, 3], [1, 0, 1, 0]] %961 := [[3, 1, 2, 5, 4], [0, 1, 0, 1]] %962 := [[2, 1, 4, 5, 3], [1, 1, 0, 0]] %963 := [[3, 1, 2, 5, 4], [0, 0, 1, 1]] %964 := [[1, 2, 4, 5, 3], [1, 1, 1, 1]] %965 := [[3, 1, 2, 4, 5], [1, 1, 1, 1]] %966 := [[1, 2, 4, 5, 3], [1, 1, 0, 1]] %967 := [[3, 1, 2, 4, 5], [1, 0, 1, 1]] %968 := [[1, 2, 4, 5, 3], [1, 1, 0, 0]] %969 := [[3, 1, 2, 4, 5], [0, 0, 1, 1]] %970 := [[3, 5, 2, 1, 4], [1, 0, 1, 1]] %971 := [[2, 5, 4, 1, 3], [1, 1, 0, 1]] %972 := [[5, 2, 3, 1, 4], [0, 0, 1, 1]] %973 := [[2, 5, 3, 4, 1], [1, 1, 0, 0]] %974 := [[2, 5, 3, 1, 4], [1, 1, 1, 1]] %975 := [[2, 5, 3, 1, 4], [0, 1, 1, 1]] %976 := [[2, 5, 3, 1, 4], [1, 1, 1, 0]] %977 := [[2, 5, 3, 1, 4], [1, 0, 1, 1]] %978 := [[2, 5, 3, 1, 4], [1, 1, 0, 1]] %979 := [[2, 5, 3, 1, 4], [0, 0, 1, 1]] %980 := [[2, 5, 3, 1, 4], [1, 1, 0, 0]] %981 := [[2, 5, 3, 1, 4], [0, 1, 1, 0]] %982 := [[2, 5, 3, 1, 4], [1, 0, 1, 0]] %983 := [[2, 5, 3, 1, 4], [0, 1, 0, 1]] %984 := [[2, 5, 3, 1, 4], [0, 0, 1, 0]] %985 := [[2, 5, 3, 1, 4], [0, 1, 0, 0]] %986 := [[2, 3, 5, 1, 4], [1, 1, 1, 1]] %987 := [[2, 5, 1, 3, 4], [1, 1, 1, 1]] %988 := [[2, 3, 5, 1, 4], [0, 1, 1, 1]] %989 := [[2, 5, 1, 3, 4], [1, 1, 1, 0]] %990 := [[2, 3, 5, 1, 4], [1, 0, 1, 1]] %991 := [[2, 5, 1, 3, 4], [1, 1, 0, 1]] %992 := [[2, 3, 5, 1, 4], [0, 0, 1, 1]] %993 := [[2, 5, 1, 3, 4], [1, 1, 0, 0]] %994 := [[2, 3, 5, 1, 4], [1, 1, 0, 1]] %995 := [[2, 5, 1, 3, 4], [1, 0, 1, 1]] %996 := [[2, 3, 5, 1, 4], [0, 1, 0, 1]] %997 := [[2, 5, 1, 3, 4], [1, 0, 1, 0]] %998 := [[2, 3, 5, 1, 4], [1, 1, 1, 0]] %999 := [[2, 5, 1, 3, 4], [0, 1, 1, 1]] %1000 := [[2, 3, 5, 1, 4], [0, 1, 1, 0]] %1001 := [[2, 5, 1, 3, 4], [0, 1, 1, 0]] %1002 := [[2, 3, 5, 1, 4], [1, 0, 1, 0]] %1003 := [[2, 5, 1, 3, 4], [0, 1, 0, 1]] %1004 := [[2, 3, 5, 1, 4], [0, 0, 1, 0]] %1005 := [[2, 5, 1, 3, 4], [0, 1, 0, 0]] %1006 := [[2, 3, 5, 1, 4], [1, 1, 0, 0]] %1007 := [[2, 5, 1, 3, 4], [0, 0, 1, 1]] %1008 := [[2, 3, 5, 1, 4], [0, 1, 0, 0]] %1009 := [[2, 5, 1, 3, 4], [0, 0, 1, 0]] %1010 := [[1, 5, 3, 2, 4], [1, 1, 1, 1]] %1011 := [[2, 4, 3, 1, 5], [1, 1, 1, 1]] %1012 := [[1, 5, 3, 2, 4], [0, 1, 1, 1]] %1013 := [[2, 4, 3, 1, 5], [1, 1, 1, 0]] %1014 := [[1, 5, 3, 2, 4], [1, 0, 1, 1]] %1015 := [[2, 4, 3, 1, 5], [1, 1, 0, 1]] %1016 := [[1, 5, 3, 2, 4], [0, 0, 1, 1]] %1017 := [[2, 4, 3, 1, 5], [1, 1, 0, 0]] %1018 := [[1, 5, 3, 2, 4], [1, 1, 1, 0]] %1019 := [[2, 4, 3, 1, 5], [0, 1, 1, 1]] %1020 := [[1, 5, 3, 2, 4], [0, 1, 1, 0]] %1021 := [[2, 4, 3, 1, 5], [0, 1, 1, 0]] %1022 := [[1, 5, 3, 2, 4], [1, 0, 1, 0]] %1023 := [[2, 4, 3, 1, 5], [0, 1, 0, 1]] %1024 := [[1, 5, 3, 2, 4], [0, 0, 1, 0]] %1025 := [[2, 4, 3, 1, 5], [0, 1, 0, 0]] %1026 := [[3, 1, 5, 2, 4], [1, 1, 0, 1]] %1027 := [[2, 4, 1, 5, 3], [1, 0, 1, 1]] %1028 := [[3, 1, 5, 2, 4], [1, 1, 0, 0]] %1029 := [[2, 4, 1, 5, 3], [0, 0, 1, 1]] %1030 := [[1, 3, 5, 2, 4], [1, 1, 1, 1]] %1031 := [[2, 4, 1, 3, 5], [1, 1, 1, 1]] %1032 := [[1, 3, 5, 2, 4], [0, 1, 1, 1]] %1033 := [[2, 4, 1, 3, 5], [1, 1, 1, 0]] %1034 := [[1, 3, 5, 2, 4], [1, 0, 1, 1]] %1035 := [[2, 4, 1, 3, 5], [1, 1, 0, 1]] %1036 := [[1, 3, 5, 2, 4], [0, 0, 1, 1]] %1037 := [[2, 4, 1, 3, 5], [1, 1, 0, 0]] %1038 := [[1, 3, 5, 2, 4], [1, 1, 0, 1]] %1039 := [[2, 4, 1, 3, 5], [1, 0, 1, 1]] %1040 := [[1, 3, 5, 2, 4], [0, 1, 0, 1]] %1041 := [[2, 4, 1, 3, 5], [1, 0, 1, 0]] %1042 := [[1, 3, 5, 2, 4], [1, 1, 1, 0]] %1043 := [[2, 4, 1, 3, 5], [0, 1, 1, 1]] %1044 := [[1, 3, 5, 2, 4], [0, 1, 1, 0]] %1045 := [[2, 4, 1, 3, 5], [0, 1, 1, 0]] %1046 := [[1, 3, 5, 2, 4], [1, 0, 1, 0]] %1047 := [[2, 4, 1, 3, 5], [0, 1, 0, 1]] %1048 := [[1, 3, 5, 2, 4], [0, 0, 1, 0]] %1049 := [[2, 4, 1, 3, 5], [0, 1, 0, 0]] %1050 := [[1, 3, 5, 2, 4], [1, 1, 0, 0]] %1051 := [[2, 4, 1, 3, 5], [0, 0, 1, 1]] %1052 := [[1, 3, 5, 2, 4], [0, 1, 0, 0]] %1053 := [[2, 4, 1, 3, 5], [0, 0, 1, 0]] %1054 := [[1, 5, 2, 3, 4], [1, 1, 1, 1]] %1055 := [[2, 3, 4, 1, 5], [1, 1, 1, 1]] %1056 := [[1, 5, 2, 3, 4], [1, 1, 1, 0]] %1057 := [[2, 3, 4, 1, 5], [0, 1, 1, 1]] %1058 := [[1, 5, 2, 3, 4], [1, 1, 0, 0]] %1059 := [[2, 3, 4, 1, 5], [0, 0, 1, 1]] %1060 := [[2, 1, 5, 3, 4], [1, 1, 1, 1]] %1061 := [[2, 3, 1, 5, 4], [1, 1, 1, 1]] %1062 := [[2, 1, 5, 3, 4], [1, 0, 1, 1]] %1063 := [[2, 3, 1, 5, 4], [1, 1, 0, 1]] %1064 := [[2, 1, 5, 3, 4], [1, 1, 1, 0]] %1065 := [[2, 3, 1, 5, 4], [0, 1, 1, 1]] %1066 := [[2, 1, 5, 3, 4], [1, 0, 1, 0]] %1067 := [[2, 3, 1, 5, 4], [0, 1, 0, 1]] %1068 := [[1, 2, 5, 3, 4], [1, 1, 1, 1]] %1069 := [[2, 3, 1, 4, 5], [1, 1, 1, 1]] %1070 := [[1, 2, 5, 3, 4], [0, 1, 1, 1]] %1071 := [[2, 3, 1, 4, 5], [1, 1, 1, 0]] %1072 := [[1, 2, 5, 3, 4], [1, 0, 1, 1]] %1073 := [[2, 3, 1, 4, 5], [1, 1, 0, 1]] %1074 := [[1, 2, 5, 3, 4], [1, 1, 1, 0]] %1075 := [[2, 3, 1, 4, 5], [0, 1, 1, 1]] %1076 := [[1, 2, 5, 3, 4], [0, 1, 1, 0]] %1077 := [[2, 3, 1, 4, 5], [0, 1, 1, 0]] %1078 := [[3, 2, 1, 5, 4], [1, 1, 1, 0]] %1079 := [[2, 1, 5, 4, 3], [0, 1, 1, 1]] %1080 := [[3, 2, 1, 5, 4], [1, 1, 0, 0]] %1081 := [[2, 1, 5, 4, 3], [0, 0, 1, 1]] %1082 := [[2, 3, 1, 5, 4], [1, 1, 1, 0]] %1083 := [[2, 1, 5, 3, 4], [0, 1, 1, 1]] %1084 := [[2, 3, 1, 5, 4], [0, 1, 1, 0]] %1085 := [[2, 1, 5, 3, 4], [0, 1, 1, 0]] %1086 := [[2, 3, 1, 5, 4], [1, 1, 0, 0]] %1087 := [[2, 1, 5, 3, 4], [0, 0, 1, 1]] %1088 := [[2, 3, 1, 5, 4], [0, 1, 0, 0]] %1089 := [[2, 1, 5, 3, 4], [0, 0, 1, 0]] %1090 := [[3, 1, 2, 5, 4], [1, 1, 1, 0]] %1091 := [[2, 1, 4, 5, 3], [0, 1, 1, 1]] %1092 := [[3, 1, 2, 5, 4], [1, 1, 0, 0]] %1093 := [[2, 1, 4, 5, 3], [0, 0, 1, 1]] %1094 := [[1, 3, 2, 5, 4], [1, 1, 1, 1]] %1095 := [[2, 1, 4, 3, 5], [1, 1, 1, 1]] %1096 := [[1, 3, 2, 5, 4], [0, 1, 1, 1]] %1097 := [[2, 1, 4, 3, 5], [1, 1, 1, 0]] %1098 := [[1, 3, 2, 5, 4], [1, 1, 0, 1]] %1099 := [[2, 1, 4, 3, 5], [1, 0, 1, 1]] %1100 := [[1, 3, 2, 5, 4], [0, 1, 0, 1]] %1101 := [[2, 1, 4, 3, 5], [1, 0, 1, 0]] %1102 := [[1, 3, 2, 5, 4], [1, 1, 1, 0]] %1103 := [[2, 1, 4, 3, 5], [0, 1, 1, 1]] %1104 := [[1, 3, 2, 5, 4], [0, 1, 1, 0]] %1105 := [[2, 1, 4, 3, 5], [0, 1, 1, 0]] %1106 := [[1, 3, 2, 5, 4], [1, 1, 0, 0]] %1107 := [[2, 1, 4, 3, 5], [0, 0, 1, 1]] %1108 := [[2, 1, 3, 5, 4], [1, 1, 1, 1]] %1109 := [[2, 1, 3, 5, 4], [1, 0, 1, 1]] %1110 := [[2, 1, 3, 5, 4], [1, 1, 0, 1]] %1111 := [[2, 1, 3, 5, 4], [1, 0, 0, 1]] %1112 := [[2, 1, 3, 5, 4], [1, 1, 1, 0]] %1113 := [[2, 1, 3, 5, 4], [0, 1, 1, 1]] %1114 := [[2, 1, 3, 5, 4], [1, 1, 0, 0]] %1115 := [[2, 1, 3, 5, 4], [0, 0, 1, 1]] %1116 := [[1, 2, 3, 5, 4], [1, 1, 1, 1]] %1117 := [[2, 1, 3, 4, 5], [1, 1, 1, 1]] %1118 := [[1, 2, 3, 5, 4], [1, 1, 0, 1]] %1119 := [[2, 1, 3, 4, 5], [1, 0, 1, 1]] %1120 := [[1, 2, 3, 5, 4], [1, 1, 1, 0]] %1121 := [[2, 1, 3, 4, 5], [0, 1, 1, 1]] %1122 := [[1, 2, 3, 5, 4], [1, 1, 0, 0]] %1123 := [[2, 1, 3, 4, 5], [0, 0, 1, 1]] %1124 := [[3, 2, 4, 1, 5], [1, 1, 1, 1]] %1125 := [[1, 5, 2, 4, 3], [1, 1, 1, 1]] %1126 := [[2, 3, 4, 1, 5], [1, 0, 1, 1]] %1127 := [[1, 5, 2, 3, 4], [1, 1, 0, 1]] %1128 := [[1, 4, 3, 2, 5], [1, 1, 1, 1]] %1129 := [[1, 4, 3, 2, 5], [0, 1, 1, 1]] %1130 := [[1, 4, 3, 2, 5], [1, 1, 1, 0]] %1131 := [[1, 4, 3, 2, 5], [0, 1, 1, 0]] %1132 := [[1, 3, 4, 2, 5], [1, 1, 1, 1]] %1133 := [[1, 4, 2, 3, 5], [1, 1, 1, 1]] %1134 := [[1, 3, 4, 2, 5], [0, 1, 1, 1]] %1135 := [[1, 4, 2, 3, 5], [1, 1, 1, 0]] %1136 := [[1, 3, 4, 2, 5], [1, 0, 1, 1]] %1137 := [[1, 4, 2, 3, 5], [1, 1, 0, 1]] %1138 := [[1, 3, 4, 2, 5], [0, 0, 1, 1]] %1139 := [[1, 4, 2, 3, 5], [1, 1, 0, 0]] %1140 := [[1, 3, 4, 2, 5], [1, 1, 1, 0]] %1141 := [[1, 4, 2, 3, 5], [0, 1, 1, 1]] %1142 := [[1, 3, 4, 2, 5], [0, 1, 1, 0]] %1143 := [[1, 4, 2, 3, 5], [0, 1, 1, 0]] %1144 := [[1, 3, 4, 2, 5], [1, 0, 1, 0]] %1145 := [[1, 4, 2, 3, 5], [0, 1, 0, 1]] %1146 := [[1, 3, 4, 2, 5], [0, 0, 1, 0]] %1147 := [[1, 4, 2, 3, 5], [0, 1, 0, 0]] %1148 := [[1, 2, 4, 3, 5], [1, 1, 1, 1]] %1149 := [[1, 3, 2, 4, 5], [1, 1, 1, 1]] %1150 := [[1, 2, 4, 3, 5], [0, 1, 1, 1]] %1151 := [[1, 3, 2, 4, 5], [1, 1, 1, 0]] %1152 := [[1, 2, 4, 3, 5], [1, 0, 1, 1]] %1153 := [[1, 3, 2, 4, 5], [1, 1, 0, 1]] %1154 := [[1, 2, 4, 3, 5], [0, 0, 1, 1]] %1155 := [[1, 3, 2, 4, 5], [1, 1, 0, 0]] %1156 := [[1, 2, 4, 3, 5], [1, 1, 1, 0]] %1157 := [[1, 3, 2, 4, 5], [0, 1, 1, 1]] %1158 := [[1, 2, 4, 3, 5], [0, 1, 1, 0]] %1159 := [[1, 3, 2, 4, 5], [0, 1, 1, 0]] %1160 := [[1, 2, 4, 3, 5], [1, 0, 1, 0]] %1161 := [[1, 3, 2, 4, 5], [0, 1, 0, 1]] %1162 := [[1, 2, 4, 3, 5], [0, 0, 1, 0]] %1163 := [[1, 3, 2, 4, 5], [0, 1, 0, 0]] %1164 := [[2, 1, 3, 4, 5], [1, 1, 0, 1]] %1165 := [[1, 2, 3, 5, 4], [1, 0, 1, 1]] %1166 := [[2, 1, 3, 4, 5], [1, 1, 0, 0]] %1167 := [[1, 2, 3, 5, 4], [0, 0, 1, 1]] %1168 := [[1, 2, 3, 4, 5], [1, 1, 1, 1]] %1169 := [[1, 2, 3, 4, 5], [0, 0, 1, 1]] %1170 := [[1, 2, 3, 4, 5], [1, 1, 0, 0]] %1171 := [[1, 2, 3, 4, 5], [1, 1, 0, 1]] %1172 := [[1, 2, 3, 4, 5], [1, 0, 1, 1]] %1173 := [[5, 3, 4, 2, 1], [1, 1, 1, 1]] %1174 := [[2, 1, 3], [1, 0]] %1175 := [[5, 4, 2, 3, 1], [1, 1, 1, 1]] %1176 := [[1, 3, 2], [0, 1]] %1177 := [[4, 3, 5, 2, 1], [0, 1, 0, 1]] %1178 := [[5, 4, 1, 3, 2], [1, 0, 1, 0]] %1179 := [[4, 3, 5, 2, 1], [0, 1, 0, 0]] %1180 := [[5, 4, 1, 3, 2], [0, 0, 1, 0]] %1181 := [[4, 2, 5, 3, 1], [0, 1, 0, 1]] %1182 := [[5, 3, 1, 4, 2], [1, 0, 1, 0]] %1183 := [[4, 2, 5, 3, 1], [0, 1, 0, 0]] %1184 := [[5, 3, 1, 4, 2], [0, 0, 1, 0]] %1185 := [[2, 5, 3, 4, 1], [1, 0, 1, 1]] %1186 := [[5, 2, 3, 1, 4], [1, 1, 0, 1]] %1187 := [[2, 5, 3, 4, 1], [0, 0, 1, 1]] %1188 := [[5, 2, 3, 1, 4], [1, 1, 0, 0]] %1189 := [[3, 2, 5, 4, 1], [0, 1, 0, 0]] %1190 := [[5, 2, 1, 4, 3], [0, 0, 1, 0]] %1191 := [[4, 3, 2, 5, 1], [1, 0, 1, 0]] %1192 := [[5, 1, 4, 3, 2], [0, 1, 0, 1]] %1193 := [[4, 3, 2, 5, 1], [0, 0, 1, 0]] %1194 := [[5, 1, 4, 3, 2], [0, 1, 0, 0]] %1195 := [[3, 4, 2, 5, 1], [1, 0, 1, 0]] %1196 := [[5, 1, 4, 2, 3], [0, 1, 0, 1]] %1197 := [[3, 4, 2, 5, 1], [0, 0, 1, 0]] %1198 := [[5, 1, 4, 2, 3], [0, 1, 0, 0]] %1199 := [[2, 4, 3, 5, 1], [1, 0, 1, 0]] %1200 := [[5, 1, 3, 2, 4], [0, 1, 0, 1]] %1201 := [[2, 4, 3, 5, 1], [0, 0, 1, 0]] %1202 := [[5, 1, 3, 2, 4], [0, 1, 0, 0]] %1203 := [[3, 2, 4, 5, 1], [0, 1, 0, 0]] %1204 := [[5, 1, 2, 4, 3], [0, 0, 1, 0]] %1205 := [[5, 4, 3, 1, 2], [1, 0, 1, 1]] %1206 := [[4, 5, 3, 2, 1], [1, 1, 0, 1]] %1207 := [[4, 5, 3, 1, 2], [1, 0, 0, 1]] %1208 := [[5, 3, 4, 1, 2], [1, 0, 1, 1]] %1209 := [[4, 5, 2, 3, 1], [1, 1, 0, 1]] %1210 := [[5, 3, 4, 1, 2], [0, 0, 1, 1]] %1211 := [[4, 5, 2, 3, 1], [1, 1, 0, 0]] %1212 := [[3, 5, 4, 1, 2], [0, 0, 1, 1]] %1213 := [[4, 5, 2, 1, 3], [1, 1, 0, 0]] %1214 := [[5, 4, 1, 3, 2], [1, 1, 1, 0]] %1215 := [[4, 3, 5, 2, 1], [0, 1, 1, 1]] %1216 := [[5, 1, 4, 3, 2], [1, 1, 0, 1]] %1217 := [[4, 3, 2, 5, 1], [1, 0, 1, 1]] %1218 := [[5, 1, 4, 3, 2], [1, 1, 0, 0]] %1219 := [[4, 3, 2, 5, 1], [0, 0, 1, 1]] %1220 := [[4, 1, 5, 3, 2], [0, 1, 0, 1]] %1221 := [[4, 3, 1, 5, 2], [1, 0, 1, 0]] %1222 := [[4, 1, 5, 3, 2], [0, 1, 1, 0]] %1223 := [[4, 3, 1, 5, 2], [0, 1, 1, 0]] %1224 := [[4, 1, 5, 3, 2], [0, 1, 0, 0]] %1225 := [[4, 3, 1, 5, 2], [0, 0, 1, 0]] %1226 := [[3, 1, 5, 4, 2], [0, 1, 0, 1]] %1227 := [[4, 2, 1, 5, 3], [1, 0, 1, 0]] %1228 := [[3, 1, 5, 4, 2], [0, 1, 1, 0]] %1229 := [[4, 2, 1, 5, 3], [0, 1, 1, 0]] %1230 := [[3, 1, 5, 4, 2], [0, 1, 0, 0]] %1231 := [[4, 2, 1, 5, 3], [0, 0, 1, 0]] %1232 := [[3, 4, 1, 5, 2], [1, 0, 1, 0]] %1233 := [[4, 1, 5, 2, 3], [0, 1, 0, 1]] %1234 := [[3, 4, 1, 5, 2], [0, 0, 1, 0]] %1235 := [[4, 1, 5, 2, 3], [0, 1, 0, 0]] %1236 := [[4, 1, 3, 5, 2], [0, 1, 1, 0]] %1237 := [[4, 1, 3, 5, 2], [0, 0, 1, 0]] %1238 := [[4, 1, 3, 5, 2], [0, 1, 0, 0]] %1239 := [[1, 4, 3, 5, 2], [1, 0, 1, 1]] %1240 := [[4, 1, 3, 2, 5], [1, 1, 0, 1]] %1241 := [[1, 4, 3, 5, 2], [0, 0, 1, 1]] %1242 := [[4, 1, 3, 2, 5], [1, 1, 0, 0]] %1243 := [[1, 4, 3, 5, 2], [1, 0, 1, 0]] %1244 := [[4, 1, 3, 2, 5], [0, 1, 0, 1]] %1245 := [[1, 4, 3, 5, 2], [0, 0, 1, 0]] %1246 := [[4, 1, 3, 2, 5], [0, 1, 0, 0]] %1247 := [[3, 1, 4, 5, 2], [0, 1, 1, 0]] %1248 := [[4, 1, 2, 5, 3], [0, 1, 1, 0]] %1249 := [[3, 1, 4, 5, 2], [0, 1, 0, 0]] %1250 := [[4, 1, 2, 5, 3], [0, 0, 1, 0]] %1251 := [[2, 5, 4, 1, 3], [1, 0, 0, 1]] %1252 := [[3, 5, 2, 1, 4], [1, 0, 0, 1]] %1253 := [[5, 4, 1, 2, 3], [1, 1, 1, 0]] %1254 := [[3, 4, 5, 2, 1], [0, 1, 1, 1]] %1255 := [[5, 1, 4, 2, 3], [1, 1, 0, 1]] %1256 := [[3, 4, 2, 5, 1], [1, 0, 1, 1]] %1257 := [[5, 1, 4, 2, 3], [1, 1, 0, 0]] %1258 := [[3, 4, 2, 5, 1], [0, 0, 1, 1]] %1259 := [[1, 5, 4, 2, 3], [1, 1, 0, 1]] %1260 := [[3, 4, 2, 1, 5], [1, 0, 1, 1]] %1261 := [[5, 2, 1, 4, 3], [1, 0, 1, 0]] %1262 := [[3, 2, 5, 4, 1], [0, 1, 0, 1]] %1263 := [[2, 5, 1, 4, 3], [1, 0, 1, 0]] %1264 := [[3, 2, 5, 1, 4], [0, 1, 0, 1]] %1265 := [[2, 5, 1, 4, 3], [0, 0, 1, 0]] %1266 := [[3, 2, 5, 1, 4], [0, 1, 0, 0]] %1267 := [[1, 5, 2, 4, 3], [1, 0, 1, 1]] %1268 := [[3, 2, 4, 1, 5], [1, 1, 0, 1]] %1269 := [[1, 5, 2, 4, 3], [0, 0, 1, 1]] %1270 := [[3, 2, 4, 1, 5], [1, 1, 0, 0]] %1271 := [[1, 5, 2, 4, 3], [1, 0, 1, 0]] %1272 := [[3, 2, 4, 1, 5], [0, 1, 0, 1]] %1273 := [[1, 5, 2, 4, 3], [0, 0, 1, 0]] %1274 := [[3, 2, 4, 1, 5], [0, 1, 0, 0]] %1275 := [[2, 4, 1, 5, 3], [1, 0, 1, 0]] %1276 := [[3, 1, 5, 2, 4], [0, 1, 0, 1]] %1277 := [[2, 4, 1, 5, 3], [0, 0, 1, 0]] %1278 := [[3, 1, 5, 2, 4], [0, 1, 0, 0]] %1279 := [[1, 4, 2, 5, 3], [1, 0, 1, 1]] %1280 := [[3, 1, 4, 2, 5], [1, 1, 0, 1]] %1281 := [[1, 4, 2, 5, 3], [0, 0, 1, 1]] %1282 := [[3, 1, 4, 2, 5], [1, 1, 0, 0]] %1283 := [[1, 4, 2, 5, 3], [1, 0, 1, 0]] %1284 := [[3, 1, 4, 2, 5], [0, 1, 0, 1]] %1285 := [[1, 4, 2, 5, 3], [0, 0, 1, 0]] %1286 := [[3, 1, 4, 2, 5], [0, 1, 0, 0]] %1287 := [[2, 1, 4, 5, 3], [0, 1, 1, 0]] %1288 := [[3, 1, 2, 5, 4], [0, 1, 1, 0]] %1289 := [[2, 1, 4, 5, 3], [0, 1, 0, 0]] %1290 := [[3, 1, 2, 5, 4], [0, 0, 1, 0]] %1291 := [[5, 3, 2, 1, 4], [1, 0, 1, 1]] %1292 := [[2, 5, 4, 3, 1], [1, 1, 0, 1]] %1293 := [[5, 3, 2, 1, 4], [0, 0, 1, 1]] %1294 := [[2, 5, 4, 3, 1], [1, 1, 0, 0]] %1295 := [[2, 5, 3, 1, 4], [1, 0, 0, 1]] %1296 := [[2, 3, 5, 1, 4], [1, 0, 0, 1]] %1297 := [[2, 5, 1, 3, 4], [1, 0, 0, 1]] %1298 := [[5, 1, 3, 2, 4], [1, 1, 0, 1]] %1299 := [[2, 4, 3, 5, 1], [1, 0, 1, 1]] %1300 := [[1, 5, 3, 2, 4], [1, 1, 0, 1]] %1301 := [[2, 4, 3, 1, 5], [1, 0, 1, 1]] %1302 := [[1, 5, 3, 2, 4], [0, 1, 0, 1]] %1303 := [[2, 4, 3, 1, 5], [1, 0, 1, 0]] %1304 := [[1, 5, 2, 3, 4], [1, 0, 1, 1]] %1305 := [[2, 3, 4, 1, 5], [1, 1, 0, 1]] %1306 := [[1, 5, 2, 3, 4], [0, 0, 1, 1]] %1307 := [[2, 3, 4, 1, 5], [1, 1, 0, 0]] %1308 := [[1, 5, 2, 3, 4], [1, 0, 1, 0]] %1309 := [[2, 3, 4, 1, 5], [0, 1, 0, 1]] %1310 := [[1, 5, 2, 3, 4], [0, 0, 1, 0]] %1311 := [[2, 3, 4, 1, 5], [0, 1, 0, 0]] %1312 := [[2, 1, 5, 3, 4], [1, 1, 0, 1]] %1313 := [[2, 3, 1, 5, 4], [1, 0, 1, 1]] %1314 := [[1, 2, 5, 3, 4], [1, 1, 0, 1]] %1315 := [[2, 3, 1, 4, 5], [1, 0, 1, 1]] %1316 := [[1, 2, 5, 3, 4], [0, 1, 0, 1]] %1317 := [[2, 3, 1, 4, 5], [1, 0, 1, 0]] %1318 := [[2, 1, 3, 5, 4], [0, 1, 1, 0]] %1319 := [[5, 4, 3, 2, 1], [1, 1, 1, 1]] %1320 := [[2, 1, 3], [0, 0]] %1321 := [[1, 3, 2], [0, 0]] %1322 := [[5, 3, 4, 2, 1], [0, 0, 1, 1]] %1323 := [[5, 4, 2, 3, 1], [1, 1, 0, 0]] %1324 := [[1, 5, 4, 3, 2], [1, 1, 0, 1]] %1325 := [[4, 3, 2, 1, 5], [1, 0, 1, 1]] %1326 := [[1, 5, 4, 3, 2], [1, 1, 0, 0]] %1327 := [[4, 3, 2, 1, 5], [0, 0, 1, 1]] %1328 := [[4, 3, 1, 5, 2], [0, 1, 0, 0]] %1329 := [[4, 1, 5, 3, 2], [0, 0, 1, 0]] %1330 := [[1, 5, 4, 2, 3], [1, 1, 0, 0]] %1331 := [[3, 4, 2, 1, 5], [0, 0, 1, 1]] %1332 := [[2, 1, 5, 4, 3], [0, 1, 1, 0]] %1333 := [[3, 2, 1, 5, 4], [0, 1, 1, 0]] %1334 := [[4, 2, 1, 5, 3], [0, 1, 0, 0]] %1335 := [[3, 1, 5, 4, 2], [0, 0, 1, 0]] %1336 := [[2, 1, 5, 3, 4], [1, 1, 0, 0]] %1337 := [[2, 3, 1, 5, 4], [0, 0, 1, 1]] %1338 := [[1, 2, 5, 3, 4], [1, 1, 0, 0]] %1339 := [[2, 3, 1, 4, 5], [0, 0, 1, 1]] %1340 := [[3, 2, 1, 5, 4], [0, 1, 0, 0]] %1341 := [[2, 1, 5, 4, 3], [0, 0, 1, 0]] %1342 := [[1, 3, 2, 5, 4], [1, 0, 1, 1]] %1343 := [[2, 1, 4, 3, 5], [1, 1, 0, 1]] %1344 := [[1, 4, 3, 2, 5], [1, 0, 1, 1]] %1345 := [[1, 4, 3, 2, 5], [1, 1, 0, 1]] %1346 := [[1, 4, 3, 2, 5], [0, 1, 0, 1]] %1347 := [[1, 4, 3, 2, 5], [1, 0, 1, 0]] %1348 := [[1, 3, 4, 2, 5], [1, 1, 0, 1]] %1349 := [[1, 4, 2, 3, 5], [1, 0, 1, 1]] %1350 := [[1, 3, 4, 2, 5], [0, 1, 0, 1]] %1351 := [[1, 4, 2, 3, 5], [1, 0, 1, 0]] %1352 := [[1, 2, 4, 3, 5], [1, 1, 0, 1]] %1353 := [[1, 3, 2, 4, 5], [1, 0, 1, 1]] %1354 := [[1, 2, 3], [1, 0]] %1355 := [[1, 2, 3], [0, 1]] %1356 := [[1, 2, 3], [0, 0]]