"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 ", 358, " equivalence classes of generalized patterns of lengths ", [3, 3, 3] "Class ", 1, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 6, 10, 20, 35, 70, 126, 252, 462, 924, 1716, 3432, 6435, 12870, 24310, 48620, 92378, 184756] "" "Class ", 2, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]]} "Class ", 3, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 6, 10, 20, 35, 70, 126, 252, 462, 924, 1716, 3432, 6435, 12870, 24310, 48620, 92378, 184756] "" "Class ", 4, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 5, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 0]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [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, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 8, 25, 96, 427, 2176, 12465, 79360, 555731, 4245504, 35135945, 313155584, 2990414715, 30460116992, 329655706465, 3777576173568, 45692713833379, 581777702256640] "" "Class ", 6, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[1, 0, 0]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {[1, 0, 0, 0]}], [[2, 1, 3], {1}, {[1, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 6, 14, 37, 107, 335, 1125, 4025, 15255, 60971, 256033, 1126106, 5173634, 24768528, 123298780, 636990571, 3409304469, 18874213273] "" "Class ", 7, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]]} "Class ", 8, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[1, 0, 0]}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0], [1, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 9, " is:" {{[[1, 2, 3], [0, 0]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {[1, 0, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[2, 1, 3], {1}, {[1, 0, 0, 0]}], [[2, 3, 1], {1}, {[1, 0, 0, 0]}], [[3, 1, 2], {}, {[1, 0, 0, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 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, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 7, 10, 19, 28, 56, 84, 174, 264, 561, 858, 1859, 2860, 6292, 9724, 21658, 33592, 75582] "" "Class ", 10, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[3, 2, 1], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[3, 2, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {[1, 0, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 1, 0, 0], [1, 0, 0, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1], [1, 0, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 0, 1], [1, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 0, 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], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 11, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [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], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 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, 3, 6, 10, 20, 35, 70, 126, 252, 462, 924, 1716, 3432, 6435, 12870, 24310, 48620, 92378, 184756] "" "Class ", 12, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 13, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 6, 10, 20, 35, 70, 126, 252, 462, 924, 1716, 3432, 6435, 12870, 24310, 48620, 92378, 184756] "" "Class ", 14, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {[0, 2]}], [[1, 2], {1, 2}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {1}, {[0, 0, 1], [0, 2, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 15, " is:" {{[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 0]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [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], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[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}, {[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]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 7, 17, 43, 110, 290, 789, 2201, 6230, 17794, 51221, 148653, 434855, 1280861, 3794207, 11293433, 33759778, 101320146] "" "Class ", 16, " is:" {{[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {2}, {[0, 0, 1], [1, 0, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 3}, {[0, 0, 0, 1], [1, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 9, 17, 33, 65, 129, 257, 513, 1025, 2049, 4097, 8193, 16385, 32769, 65537, 131073, 262145] "" "Class ", 17, " is:" {{[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 1, 0]}], [[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, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 18, " is:" {{[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1], [1, 0, 0]}], [[2, 1], {1}, {[0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 19, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 6, 10, 20, 35, 70, 126, 252, 462, 924, 1716, 3432, 6435, 12870, 24310, 48620, 92378, 184756] "" "Class ", 20, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]]} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 1, 0]}], [[3, 1, 2], {1}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 21, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 22, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 0]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [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, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 23, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[1, 0, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 24, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 0]]} {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {[0, 0, 1, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 25, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 1]]} {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {[0, 0, 1, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 26, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 0]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 6, 13, 29, 72, 185, 499, 1414, 4132, 12554, 39332, 126815, 420769, 1430790, 4986139, 17772536, 64708212, 240482750] "" "Class ", 27, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 28, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 29, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 30, " is:" {{%2, [[1, 3, 2], [0, 0]], %1}, {%2, [[2, 1, 3], [0, 0]], %1}, {%2, [[2, 3, 1], [0, 0]], %1}, {%2, [[3, 1, 2], [0, 0]], %1}} %1 := [[3, 2, 1], [0, 0]] %2 := [[1, 2, 3], [0, 0]] {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [0, 0]]} "For the class ", {{%2, [[1, 3, 2], [0, 0]], %1}, {%2, [[2, 1, 3], [0, 0]], %1}, {%2, [[2, 3, 1], [0, 0]], %1}, {%2, [[3, 1, 2], [0, 0]], %1}}, " the pattern set ", {%2, [[1, 3, 2], [0, 0]], %1}, " has scheme:" %1 := [[3, 2, 1], [0, 0]] %2 := [[1, 2, 3], [0, 0]] {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[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], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 11, 23, 63, 153, 489, 1329, 4785, 14235, 56475, 181215, 780255, 2672145, 12348945, 44781345, 220253985, 840523635] "" "Class ", 31, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[1, 0, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[1, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 32, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[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, 2, 3}, {[0, 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, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 33, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {[1, 0, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {[1, 0, 0, 0]}], [[2, 3, 1], {1}, {[1, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 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, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 34, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 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, 4, 9, 21, 51, 127, 323, 835, 2188, 5798, 15511, 41835, 113634, 310572, 853467, 2356779, 6536382, 18199284, 50852019] "" "Class ", 35, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 36, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 37, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 38, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0], [1, 0, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 39, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 0]]} {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 40, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 1]]} {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {[0, 0, 1, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 41, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 0]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 1, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 6, 12, 25, 54, 119, 267, 608, 1401, 3261, 7656, 18108, 43107, 103204, 248334, 600250, 1456752, 3548351] "" "Class ", 42, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 43, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 1, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 44, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 45, " is:" {{%2, [[1, 3, 2], [0, 1]], %1}, {%2, [[2, 1, 3], [1, 0]], %1}, {%2, [[2, 3, 1], [1, 0]], %1}, {%2, [[3, 1, 2], [0, 1]], %1}} %1 := [[3, 2, 1], [0, 0]] %2 := [[1, 2, 3], [0, 0]] {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [0, 0]]} "For the class ", {{%2, [[1, 3, 2], [0, 1]], %1}, {%2, [[2, 1, 3], [1, 0]], %1}, {%2, [[2, 3, 1], [1, 0]], %1}, {%2, [[3, 1, 2], [0, 1]], %1}}, " the pattern set ", {%2, [[1, 3, 2], [0, 1]], %1}, " has scheme:" %1 := [[3, 2, 1], [0, 0]] %2 := [[1, 2, 3], [0, 0]] {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 1, 0]}], [[3, 1, 2], {1}, {[0, 1, 0, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 7, 10, 19, 28, 56, 84, 174, 264, 561, 858, 1859, 2860, 6292, 9724, 21658, 33592] "" "Class ", 46, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {[1, 0, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 47, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 1, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 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, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3] "" "Class ", 48, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {}, {[1, 0, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 1, 0], [1, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 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, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 49, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 50, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 0]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [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, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 51, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[1, 0, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 52, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 53, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 1]]} {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1], [0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 54, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 0]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 6, 13, 29, 72, 185, 499, 1414, 4132, 12554, 39332, 126815, 420769, 1430790, 4986139, 17772536, 64708212, 240482750] "" "Class ", 55, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 56, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 57, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 58, " is:" {{%2, [[1, 3, 2], [1, 0]], %1}, {%2, [[2, 1, 3], [0, 1]], %1}, {%2, [[2, 3, 1], [0, 1]], %1}, {%2, [[3, 1, 2], [1, 0]], %1}} %1 := [[3, 2, 1], [0, 0]] %2 := [[1, 2, 3], [0, 0]] {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [0, 0]]} "For the class ", {{%2, [[1, 3, 2], [1, 0]], %1}, {%2, [[2, 1, 3], [0, 1]], %1}, {%2, [[2, 3, 1], [0, 1]], %1}, {%2, [[3, 1, 2], [1, 0]], %1}}, " the pattern set ", {%2, [[1, 3, 2], [1, 0]], %1}, " has scheme:" %1 := [[3, 2, 1], [0, 0]] %2 := [[1, 2, 3], [0, 0]] {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[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], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 11, 23, 63, 153, 489, 1329, 4785, 14235, 56475, 181215, 780255, 2672145, 12348945, 44781345, 220253985, 840523635] "" "Class ", 59, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[1, 0, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[1, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 60, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[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, 2, 3}, {[0, 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, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 61, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {[1, 0, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {[1, 0, 0, 0]}], [[2, 3, 1], {1}, {[1, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 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, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 62, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 0]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 63, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0], [1, 0, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 64, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 65, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0], [1, 0, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 66, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 0]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 1, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 6, 12, 25, 54, 119, 267, 608, 1401, 3261, 7656, 18108, 43107, 103204, 248334, 600250, 1456752, 3548351] "" "Class ", 67, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 68, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 1, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 69, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 70, " is:" {{%2, [[1, 3, 2], [1, 1]], %1}, {%2, [[2, 1, 3], [1, 1]], %1}, {%2, [[2, 3, 1], [1, 1]], %1}, {%2, [[3, 1, 2], [1, 1]], %1}} %1 := [[3, 2, 1], [0, 0]] %2 := [[1, 2, 3], [0, 0]] {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [0, 0]]} "For the class ", {{%2, [[1, 3, 2], [1, 1]], %1}, {%2, [[2, 1, 3], [1, 1]], %1}, {%2, [[2, 3, 1], [1, 1]], %1}, {%2, [[3, 1, 2], [1, 1]], %1}}, " the pattern set ", {%2, [[1, 3, 2], [1, 1]], %1}, " has scheme:" %1 := [[3, 2, 1], [0, 0]] %2 := [[1, 2, 3], [0, 0]] {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 1, 0]}], [[3, 1, 2], {1}, {[0, 1, 0, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 7, 10, 19, 28, 56, 84, 174, 264, 561, 858, 1859, 2860, 6292, 9724, 21658, 33592] "" "Class ", 71, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {[1, 0, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 72, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 1, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 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, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3] "" "Class ", 73, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {[1, 0, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 74, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 6, 12, 25, 54, 119, 267, 608, 1401, 3261, 7656, 18108, 43107, 103204, 248334, 600250, 1456752, 3548351] "" "Class ", 75, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 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, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 7, 19, 60, 216, 861, 3764, 17882, 91475, 500552, 2914400, 17970128, 116869122, 798903161, 5722919865, 42845367159, 334438321467, 2715980874793] "" "Class ", 76, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 6, 12, 25, 54, 119, 267, 608, 1401, 3261, 7656, 18108, 43107, 103204, 248334, 600250, 1456752, 3548351] "" "Class ", 77, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[1, 0, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 11, 23, 63, 153, 489, 1329, 4785, 14235, 56475, 181215, 780255, 2672145, 12348945, 44781345, 220253985, 840523635] "" "Class ", 78, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 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, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1, 2, 3}, {[0, 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, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 7, 10, 19, 28, 56, 84, 174, 264, 561, 858, 1859, 2860, 6292, 9724, 21658, 33592] "" "Class ", 79, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {[1, 0, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[2, 1, 3], {1}, {[1, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 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, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 7, 10, 19, 28, 56, 84, 174, 264, 561, 858, 1859, 2860, 6292, 9724, 21658, 33592] "" "Class ", 80, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 9, 21, 51, 127, 323, 835, 2188, 5798, 15511, 41835, 113634, 310572, 853467, 2356779, 6536382, 18199284, 50852019] "" "Class ", 81, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[1, 0, 0]}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0], [1, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 82, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[1, 0, 0]}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0], [1, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 83, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[1, 0, 0]}], [[2, 1], {1}, {[1, 0, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 11, 23, 63, 153, 489, 1329, 4785, 14235, 56475, 181215, 780255, 2672145, 12348945, 44781345, 220253985, 840523635] "" "Class ", 84, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[1, 0, 0]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {[1, 0, 0, 0]}], [[2, 1, 3], {1}, {[1, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[1, 0, 0, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 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, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 7, 10, 19, 28, 56, 84, 174, 264, 561, 858, 1859, 2860, 6292, 9724, 21658, 33592] "" "Class ", 85, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[1, 0, 0]}], [[2, 1], {}, {[1, 0, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[2, 1, 3], {1}, {[1, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 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, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 7, 10, 19, 28, 56, 84, 174, 264, 561, 858, 1859, 2860, 6292, 9724, 21658, 33592] "" "Class ", 86, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]]} {[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[1, 0, 0]}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0], [1, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 87, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 1]]} {[[1, 2, 3], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {[0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 1, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 7, 10, 19, 28, 56, 84, 174, 264, 561, 858, 1859, 2860, 6292, 9724, 21658, 33592] "" "Class ", 88, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 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}, {}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1, 2, 3}, {[0, 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, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3] "" "Class ", 89, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {[1, 0, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[2, 1, 3], {2}, {[1, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 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, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3] "" "Class ", 90, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 1]]} {[[1, 2, 3], [0, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {[0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 1, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 7, 10, 19, 28, 56, 84, 174, 264, 561, 858, 1859, 2860, 6292, 9724, 21658, 33592] "" "Class ", 91, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[1, 0, 0]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {[1, 0, 0, 0]}], [[2, 1, 3], {1}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[1, 0, 0, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 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, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3] "" "Class ", 92, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[1, 0, 0]}], [[2, 1], {}, {[1, 0, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[2, 1, 3], {1}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 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, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3] "" "Class ", 93, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]]}, {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]]}, {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[1, 3, 2], [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, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 9, 21, 51, 127, 323, 835, 2188, 5798, 15511, 41835, 113634, 310572, 853467, 2356779, 6536382, 18199284, 50852019] "" "Class ", 94, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]]}, {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]]}, {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 95, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[1, 3, 2], [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, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 9, 21, 51, 127, 323, 835, 2188, 5798, 15511, 41835, 113634, 310572, 853467, 2356779, 6536382, 18199284, 50852019] "" "Class ", 96, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]]}, {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]]}, {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 97, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[2, 3, 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], {1, 2, 3}, {[0, 0, 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], {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, 4, 9, 24, 73, 242, 861, 3274, 13226, 56386, 252452, 1182764, 5781011, 29398506, 155187621, 848657506, 4799383918, 28023958266, 168712174828] "" "Class ", 98, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1], [1, 0, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [1, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 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], {3}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 99, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 0]]} {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 1, 0]}], [[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, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191] "" "Class ", 100, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 1]]} {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191] "" "Class ", 101, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]], [[3, 2, 1], [0, 1]]} "For the class ", {{%3, %2, %1}, {%3, %2, [[3, 2, 1], [1, 0]]}, {%3, %1, [[3, 2, 1], [1, 0]]}, {%2, %1, [[3, 2, 1], [1, 0]]}}, " the pattern set ", {%3, %2, %1}, " has scheme:" %1 := [[3, 2, 1], [0, 1]] %2 := [[1, 2, 3], [1, 0]] %3 := [[1, 2, 3], [0, 1]] {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {[1, 0, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 1, 0, 0], [1, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [1, 0, 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], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 5, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 102, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [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], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 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, 3, 6, 10, 20, 35, 70, 126, 252, 462, 924, 1716, 3432, 6435, 12870, 24310, 48620, 92378, 184756] "" "Class ", 103, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 6, 10, 20, 35, 70, 126, 252, 462, 924, 1716, 3432, 6435, 12870, 24310, 48620, 92378, 184756] "" "Class ", 104, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 1, 0]}], [[3, 1, 2], {1}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 105, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 106, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[2, 3, 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], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 107, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1], [1, 0, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 108, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 109, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 110, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [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], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 10, 20, 40, 84, 180, 387, 845, 1870, 4163, 9334, 21091, 47913, 109356, 250801, 577563, 1334750] "" "Class ", 111, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 112, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [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], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 113, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 114, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {[1, 0, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 115, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[3, 2, 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], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 116, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {[1, 0, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1], [1, 0, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 0, 1], [1, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 117, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 118, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 119, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {1}, {[0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 120, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 1, 0]}], [[3, 1, 2], {1}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 121, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {1}, {[0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 122, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 123, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1], [0, 1, 0], [1, 0, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 124, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 125, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {[0, 0, 1, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 126, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 9, 16, 28, 49, 86, 151, 265, 465, 816, 1432, 2513, 4410, 7739, 13581, 23833, 41824] "" "Class ", 127, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {1}, {[0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 128, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 129, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {1}, {[0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 130, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {1}, {[1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 131, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 132, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {}, {[1, 0, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 133, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [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], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 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, 3, 6, 10, 20, 35, 70, 126, 252, 462, 924, 1716, 3432, 6435, 12870, 24310, 48620, 92378, 184756] "" "Class ", 134, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 6, 10, 20, 35, 70, 126, 252, 462, 924, 1716, 3432, 6435, 12870, 24310, 48620, 92378, 184756] "" "Class ", 135, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 136, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 137, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 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], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 138, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1], [1, 0, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 139, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 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], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 140, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 1]]} {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1], [0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 141, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [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], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 10, 20, 40, 84, 180, 387, 845, 1870, 4163, 9334, 21091, 47913, 109356, 250801, 577563, 1334750] "" "Class ", 142, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 143, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [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], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 144, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 145, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {[1, 0, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 146, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 2, 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], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 147, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {[1, 0, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1], [1, 0, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 0, 1], [1, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 148, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 149, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {1}, {[0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 150, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 151, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {1}, {[0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 152, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 153, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1], [0, 1, 0], [1, 0, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 154, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 155, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1], [0, 1, 0], [1, 0, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 156, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 9, 16, 28, 49, 86, 151, 265, 465, 816, 1432, 2513, 4410, 7739, 13581, 23833, 41824] "" "Class ", 157, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {1}, {[0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 158, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 159, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {1}, {[0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 160, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {1}, {[1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 161, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 162, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {1}, {[1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 163, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 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], {1, 2}, {[0, 0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}], [[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, 3, 6, 13, 29, 72, 185, 499, 1414, 4132, 12554, 39332, 126815, 420769, 1430790, 4986139, 17772536, 64708212, 240482750] "" "Class ", 164, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1], [1, 0, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0], [1, 0, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 165, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 166, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 167, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 168, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {[0, 1, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 169, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 170, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {[0, 1, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 171, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {[1, 0, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0], [1, 0, 0, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 172, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 173, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {[1, 0, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [ [3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 174, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 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, 4, 9, 21, 51, 127, 323, 835, 2188, 5798, 15511, 41835, 113634, 310572, 853467, 2356779, 6536382, 18199284, 50852019] "" "Class ", 175, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 6, 13, 29, 72, 185, 499, 1414, 4132, 12554, 39332, 126815, 420769, 1430790, 4986139, 17772536, 64708212, 240482750] "" "Class ", 176, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1], [1, 0, 0]}], [[2, 1], {1}, {[0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 177, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 178, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1], [1, 0, 0]}], [[2, 1], {1}, {[0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 179, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 180, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 0, 1], [0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 181, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 182, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 0, 1], [0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 183, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 0, 1], [1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 184, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 185, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {[0, 0, 1], [1, 0, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 186, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 0]]} {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 1, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 6, 12, 25, 54, 119, 267, 608, 1401, 3261, 7656, 18108, 43107, 103204, 248334, 600250, 1456752, 3548351] "" "Class ", 187, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]]} {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 1, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 188, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 189, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 190, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 0]]} {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 191, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {[0, 1, 0]}], [[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, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 192, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 193, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {[0, 1, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 194, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {[1, 0, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1], [0, 1, 0, 0], [1, 0, 0, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {2}, {[0, 0, 0, 1], [1, 0, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0], [1, 0, 0, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3] "" "Class ", 195, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 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], {}, {[0, 0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 0, 0, 0]}], [[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, 4}, {[0, 0, 0, 0, 0]}], [[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, 0]}], [[2, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {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, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 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, 3, 4, 5}, {[0, 0, 0, 0, 0, 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, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 196, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {[1, 0, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {[0, 0, 0, 1], [0, 1, 0, 0], [1, 0, 0, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 0, 1], [1, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 0, 0, 0]}], [[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, 0]}], [[3, 4, 1, 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], [1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 197, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 0]]} {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 1, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 6, 12, 25, 54, 119, 267, 608, 1401, 3261, 7656, 18108, 43107, 103204, 248334, 600250, 1456752, 3548351] "" "Class ", 198, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1], [1, 0, 0]}], [[2, 1], {1}, {[0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 199, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 200, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {[1, 1]}], [[1, 2], {1, 2}, {[0, 0, 1], [1, 0, 0]}], [[2, 1], {1}, {[0, 0, 1], [1, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 201, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {[0, 0, 1]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 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]}], [[2, 4, 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, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 202, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {2}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 0, 1], [0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 203, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {[0, 0, 1]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 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]}], [[2, 4, 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, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 204, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 0, 1], [0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 205, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 0, 1], [1, 0, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1], [0, 1, 0, 0], [1, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0], [1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3] "" "Class ", 206, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {[0, 0, 1]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 0, 0, 0]}], [[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, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 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, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 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, 3, 4, 5}, {[0, 0, 0, 0, 0, 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, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 207, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1], [1, 1, 0]}], [[2, 1], {}, {[0, 0, 1], [1, 0, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 208, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [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], {1}, {[0, 0, 0, 1]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 7, 19, 60, 216, 861, 3740, 17620, 89517, 486202, 2805258, 17131844, 110363697, 747148729, 5298526088, 39263064620, 303332363506, 2437946381197] "" "Class ", 209, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 12, 17, 23, 30, 38, 47, 57, 68, 80, 93, 107, 122, 138, 155, 173 ] "" "Class ", 210, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [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], {1}, {[0, 0, 0, 1]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 6, 13, 28, 59, 122, 249, 504, 1015, 2038, 4085, 8180, 16371, 32754, 65521, 131056, 262127, 524270] "" "Class ", 211, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 12, 17, 23, 30, 38, 47, 57, 68, 80, 93, 107, 122, 138, 155, 173 ] "" "Class ", 212, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {[1, 0, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {[0, 0, 0, 1], [0, 1, 0, 0], [1, 0, 0, 0]}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1], [1, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 213, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 214, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1], [1, 0, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1], [1, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 6, 14, 36, 104, 332, 1136, 4120, 15844, 64524, 276872, 1245112, 5846876, 28605084, 145533600, 768508280, 4203886116, 23778973484] "" "Class ", 215, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1], [1, 0, 0]}], [[2, 1], {1}, {[0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 216, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1], [1, 0, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1], [1, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 9, 17, 33, 65, 129, 257, 513, 1025, 2049, 4097, 8193, 16385, 32769, 65537, 131073, 262145] "" "Class ", 217, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1], [1, 0, 0]}], [[2, 1], {1}, {[0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 218, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1], [1, 0, 0]}], [[2, 1], {}, {[1, 0, 0]}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1], [1, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 219, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 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, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 3, 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, 3, 5, 9, 16, 28, 49, 86, 151, 265, 465, 816, 1432, 2513, 4410, 7739, 13581, 23833, 41824] "" "Class ", 220, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 1, 0]}], [[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, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 221, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[1, 0, 0]}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 1, 0], [1, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 222, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 1, 0]}], [[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, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 223, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {[1, 0, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {[0, 0, 0, 1], [0, 1, 0, 0], [1, 0, 0, 0]}], [[2, 1, 3], {2}, {[0, 0, 0, 1], [1, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 224, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 0]]} {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 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, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 3, 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, 3, 5, 9, 16, 28, 49, 86, 151, 265, 465, 816, 1432, 2513, 4410, 7739, 13581, 23833, 41824] "" "Class ", 225, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1], [1, 0, 0]}], [[2, 1], {1}, {[0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 226, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 0]]} {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[1, 0, 0]}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 1, 0], [1, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 227, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1], [1, 0, 0]}], [[2, 1], {1}, {[0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 228, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1], [1, 0, 0]}], [[2, 1], {}, {[1, 0, 0]}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1], [0, 1, 0, 0], [1, 0, 0, 0]}], [ [3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 229, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {[1, 0, 0]}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1], [1, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 230, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191] "" "Class ", 231, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 1, 0], [1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 232, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {[1, 0, 0]}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1], [1, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 233, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 1]]} "For the class ", { {[[1, 2, 3], [0, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {[2, 0]}], [[1, 2], {1, 2}, {[0, 0, 1], [0, 2, 0], [1, 1, 0], [2, 0, 0]}], [[2, 1], {1}, {[0, 1, 0], [1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 234, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 6, 10, 20, 35, 70, 126, 252, 462, 924, 1716, 3432, 6435, 12870, 24310, 48620, 92378, 184756] "" "Class ", 235, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [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], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 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, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 236, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 237, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 0]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[2, 3, 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], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 238, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1], [1, 0, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 239, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 0]]} {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {[0, 1, 0]}], [[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, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 240, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 1]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1], [1, 0, 0]}], [[2, 1], {1}, {[0, 1, 1]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 241, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 0]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [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], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 10, 20, 40, 84, 180, 387, 845, 1870, 4163, 9334, 21091, 47913, 109356, 250801, 577563, 1334750] "" "Class ", 242, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 243, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 0]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [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], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 244, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 245, " is:" {{%2, [[1, 3, 2], [0, 0]], %1}, {%2, [[2, 1, 3], [0, 0]], %1}, {%2, [[2, 3, 1], [0, 0]], %1}, {%2, [[3, 1, 2], [0, 0]], %1}} %1 := [[3, 2, 1], [1, 1]] %2 := [[1, 2, 3], [1, 1]] {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]], [[3, 2, 1], [1, 1]]} "For the class ", {{%2, [[1, 3, 2], [0, 0]], %1}, {%2, [[2, 1, 3], [0, 0]], %1}, {%2, [[2, 3, 1], [0, 0]], %1}, {%2, [[3, 1, 2], [0, 0]], %1}}, " the pattern set ", {%2, [[1, 3, 2], [0, 0]], %1}, " has scheme:" %1 := [[3, 2, 1], [1, 1]] %2 := [[1, 2, 3], [1, 1]] {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1], [0, 2, 0]}], [[2, 1], {1}, {[0, 2, 0], [1, 0, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 2, 0], [0, 1, 1, 0], [0, 2, 0, 0], [1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 246, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 247, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {1}, {[0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 248, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {1}, {[0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 249, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 250, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1], [0, 1, 0], [1, 0, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 251, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 0]]} {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {[0, 1, 0]}], [[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, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 252, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 1]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1], [0, 1, 0], [1, 0, 0]}], [[2, 1], {1}, {[0, 1, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 253, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 0]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 9, 16, 28, 49, 86, 151, 265, 465, 816, 1432, 2513, 4410, 7739, 13581, 23833, 41824] "" "Class ", 254, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {1}, {[0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 255, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 0]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 256, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {1}, {[0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 257, " is:" {{%2, [[1, 3, 2], [0, 1]], %1}, {%2, [[2, 1, 3], [1, 0]], %1}, {%2, [[2, 3, 1], [1, 0]], %1}, {%2, [[3, 1, 2], [0, 1]], %1}} %1 := [[3, 2, 1], [1, 1]] %2 := [[1, 2, 3], [1, 1]] {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]], [[3, 2, 1], [1, 1]]} "For the class ", {{%2, [[1, 3, 2], [0, 1]], %1}, {%2, [[2, 1, 3], [1, 0]], %1}, {%2, [[2, 3, 1], [1, 0]], %1}, {%2, [[3, 1, 2], [0, 1]], %1}}, " the pattern set ", {%2, [[1, 3, 2], [0, 1]], %1}, " has scheme:" %1 := [[3, 2, 1], [1, 1]] %2 := [[1, 2, 3], [1, 1]] {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {1}, {[0, 2, 0], [1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 258, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946] "" "Class ", 259, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 0]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 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], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 260, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1], [1, 0, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 261, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 0]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 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], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 262, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 1]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1], [1, 0, 0]}], [[2, 1], {1}, {[0, 1, 1]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 263, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 0]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [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], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 10, 20, 40, 84, 180, 387, 845, 1870, 4163, 9334, 21091, 47913, 109356, 250801, 577563, 1334750] "" "Class ", 264, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 265, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 0]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [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], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 266, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 267, " is:" {{%2, [[1, 3, 2], [1, 0]], %1}, {%2, [[2, 1, 3], [0, 1]], %1}, {%2, [[2, 3, 1], [0, 1]], %1}, {%2, [[3, 1, 2], [1, 0]], %1}} %1 := [[3, 2, 1], [1, 1]] %2 := [[1, 2, 3], [1, 1]] {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [1, 1]]} "For the class ", {{%2, [[1, 3, 2], [1, 0]], %1}, {%2, [[2, 1, 3], [0, 1]], %1}, {%2, [[2, 3, 1], [0, 1]], %1}, {%2, [[3, 1, 2], [1, 0]], %1}}, " the pattern set ", {%2, [[1, 3, 2], [1, 0]], %1}, " has scheme:" %1 := [[3, 2, 1], [1, 1]] %2 := [[1, 2, 3], [1, 1]] {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1], [0, 2, 0]}], [[2, 1], {1}, {[0, 2, 0], [1, 0, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 2, 0], [0, 1, 1, 0], [0, 2, 0, 0], [1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 268, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 0]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {[0, 2]}], [[1, 2], {}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {1}, {[0, 0, 2], [0, 1, 1], [0, 2, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 269, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 1]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {[0, 2]}], [[1, 2], {1, 2}, {[0, 0, 1], [0, 1, 0], [1, 0, 0]}], [[2, 1], {1}, {[0, 0, 2], [0, 1, 1], [0, 2, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 270, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 0]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {[0, 2]}], [[1, 2], {}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {1}, {[0, 0, 2], [0, 1, 1], [0, 2, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 271, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 0]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {[0, 2]}], [[1, 2], {1}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {}, {[0, 0, 2], [0, 1, 1], [0, 2, 0]}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 0, 2], [0, 0, 1, 1], [0, 0, 2, 0], [0, 1, 0, 1], [0, 1, 1, 0], [0, 2, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 9, 16, 28, 49, 86, 151, 265, 465, 816, 1432, 2513, 4410, 7739, 13581, 23833, 41824] "" "Class ", 272, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {[0, 2]}], [[1, 2], {1}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {1}, {[0, 0, 2], [0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 273, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 0]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {[0, 2]}], [[1, 2], {1}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {}, {[0, 0, 2], [0, 1, 1], [0, 2, 0]}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {2}, {[0, 0, 0, 2], [0, 0, 1, 1], [0, 0, 2, 0], [0, 1, 0, 1], [0, 1, 1, 0], [0, 2, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 274, " is:" {{%2, [[1, 3, 2], [1, 1]], %1}, {%2, [[2, 1, 3], [1, 1]], %1}, {%2, [[2, 3, 1], [1, 1]], %1}, {%2, [[3, 1, 2], [1, 1]], %1}} %1 := [[3, 2, 1], [1, 1]] %2 := [[1, 2, 3], [1, 1]] {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[3, 2, 1], [1, 1]]} "For the class ", {{%2, [[1, 3, 2], [1, 1]], %1}, {%2, [[2, 1, 3], [1, 1]], %1}, {%2, [[2, 3, 1], [1, 1]], %1}, {%2, [[3, 1, 2], [1, 1]], %1}}, " the pattern set ", {%2, [[1, 3, 2], [1, 1]], %1}, " has scheme:" %1 := [[3, 2, 1], [1, 1]] %2 := [[1, 2, 3], [1, 1]] {[[], {}, {}], [[1], {}, {[0, 2]}], [[1, 2], {1}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {1, 2}, {[0, 0, 2], [0, 1, 1], [0, 2, 0], [1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 275, " is:" {{[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 1, 0]}], [[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, 3}, {[0, 0, 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], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 12, 17, 23, 30, 38, 47, 57, 68, 80, 93, 107, 122, 138, 155, 173 ] "" "Class ", 276, " is:" {{[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [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], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[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], {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]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 6, 13, 28, 59, 122, 249, 504, 1015, 2038, 4085, 8180, 16371, 32754, 65521, 131056, 262127, 524270] "" "Class ", 277, " is:" {{[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 8, 12, 17, 23, 30, 38, 47, 57, 68, 80, 93, 107, 122, 138, 155, 173 ] "" "Class ", 278, " is:" {{[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]]} {[[1, 2, 3], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 1, 0]}], [[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, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191] "" "Class ", 279, " is:" {{[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {2}, {[0, 0, 1], [1, 0, 0]}], [[2, 1], {1}, {[0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 280, " is:" {{[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1], [1, 0, 0]}], [[2, 1], {1}, {[0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 281, " is:" {{[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 1, 0]}], [[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, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 282, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 0]]} "For the class ", {{%3, %2, %1}, {%3, %2, [[3, 1, 2], [0, 0]]}, {%3, %1, [[3, 1, 2], [0, 0]]}, {%2, %1, [[3, 1, 2], [0, 0]]}}, " the pattern set ", {%3, %2, %1}, " has scheme:" %1 := [[2, 3, 1], [0, 0]] %2 := [[2, 1, 3], [0, 0]] %3 := [[1, 3, 2], [0, 0]] {[[], {}, {}], [[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}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 9, 17, 33, 65, 129, 257, 513, 1025, 2049, 4097, 8193, 16385, 32769, 65537, 131073, 262145] "" "Class ", 283, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]]} "For the class ", { {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[1, 0, 0]}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1}, {[1, 0, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 9, 17, 33, 65, 129, 257, 513, 1025, 2049, 4097, 8193, 16385, 32769, 65537, 131073, 262145] "" "Class ", 284, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 0]]} {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {[0, 1, 0]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 9, 17, 33, 65, 129, 257, 513, 1025, 2049, 4097, 8193, 16385, 32769, 65537, 131073, 262145] "" "Class ", 285, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 1]]} {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {[0, 1, 0]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 9, 17, 33, 65, 129, 257, 513, 1025, 2049, 4097, 8193, 16385, 32769, 65537, 131073, 262145] "" "Class ", 286, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]]} {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]]} "For the class ", { {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 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, 4, 9, 22, 57, 154, 429, 1223, 3550, 10455, 31160, 93802, 284789, 871008, 2681019, 8298933, 25817396, 80674902, 253106837] "" "Class ", 287, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]]} "For the class ", { {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 288, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]]} "For the class ", { {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[1, 0, 0]}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 289, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]]} {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]]} "For the class ", { {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 290, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]]} "For the class ", { {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[1, 0, 0]}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 291, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 0]]} "For the class ", { {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {[0, 0, 1]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 9, 17, 33, 65, 129, 257, 513, 1025, 2049, 4097, 8193, 16385, 32769, 65537, 131073, 262145] "" "Class ", 292, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1], [0, 1, 0]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 9, 17, 33, 65, 129, 257, 513, 1025, 2049, 4097, 8193, 16385, 32769, 65537, 131073, 262145] "" "Class ", 293, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 0]]} "For the class ", { {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {[0, 0, 1]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 9, 17, 33, 65, 129, 257, 513, 1025, 2049, 4097, 8193, 16385, 32769, 65537, 131073, 262145] "" "Class ", 294, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1], [0, 1, 0]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 9, 17, 33, 65, 129, 257, 513, 1025, 2049, 4097, 8193, 16385, 32769, 65537, 131073, 262145] "" "Class ", 295, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 0]]} {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 296, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]]} {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 0]]} "For the class ", { {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 297, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 0]]} {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {[0, 1, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 298, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]]} {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {[0, 1, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 299, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 0]]} {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 0]]} "For the class ", { {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 9, 17, 33, 65, 129, 257, 513, 1025, 2049, 4097, 8193, 16385, 32769, 65537, 131073, 262145] "" "Class ", 300, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 1]]} {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 0]]} "Class ", 301, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 0]]} "For the class ", { {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 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}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 9, 17, 33, 65, 129, 257, 513, 1025, 2049, 4097, 8193, 16385, 32769, 65537, 131073, 262145] "" "Class ", 302, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {[0, 1, 0]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 9, 17, 33, 65, 129, 257, 513, 1025, 2049, 4097, 8193, 16385, 32769, 65537, 131073, 262145] "" "Class ", 303, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 0]]} {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 304, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]]} "For the class ", { {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[1, 0, 0]}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 305, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 0]]} {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {[0, 1, 0]}], [[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, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 306, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 1]]} "For the class ", { {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {[1, 1]}], [[1, 2], {}, {[0, 1, 1], [1, 0, 0]}], [[2, 1], {1}, {[0, 0, 1], [1, 1, 0]}], [[1, 2, 3], {1}, {[0, 0, 1, 1], [0, 1, 0, 0], [1, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 307, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 0]]} {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 0]]} "For the class ", { {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 9, 17, 33, 65, 129, 257, 513, 1025, 2049, 4097, 8193, 16385, 32769, 65537, 131073, 262145] "" "Class ", 308, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 1]]} {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 0]]} "For the class ", { {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 9, 17, 33, 65, 129, 257, 513, 1025, 2049, 4097, 8193, 16385, 32769, 65537, 131073, 262145] "" "Class ", 309, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 0]]} {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]]} "For the class ", { {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0], [1, 0, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 9, 17, 33, 65, 129, 257, 513, 1025, 2049, 4097, 8193, 16385, 32769, 65537, 131073, 262145] "" "Class ", 310, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1], [0, 1, 0]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 5, 9, 17, 33, 65, 129, 257, 513, 1025, 2049, 4097, 8193, 16385, 32769, 65537, 131073, 262145] "" "Class ", 311, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]]} {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 0]]} "For the class ", { {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 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], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 312, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[1, 0, 0]}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 313, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]]} "For the class ", { {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[1, 0, 0]}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {[1, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 314, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[1, 0, 0]}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 315, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]]} {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 0]]} "Class ", 316, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 0]]} {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]]} "For the class ", { {[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {[0, 0, 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, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 317, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]]} {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 0]]} "For the class ", { {[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {[0, 0, 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, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 318, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[1, 0, 0]}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 319, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 0]]} {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]]} "For the class ", { {[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {[0, 0, 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, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 320, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[1, 0, 0]}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 321, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]} "For the class ", { {[[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 9, 22, 57, 154, 429, 1223, 3550, 10455, 31160, 93802, 284789, 871008, 2681019, 8298933, 25817396, 80674902, 253106837] "" "Class ", 322, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]]} "For the class ", { {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {[0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 323, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 0]]} {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]]} "For the class ", { {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {[0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 324, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]]} "For the class ", { {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {[0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 325, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]]} "For the class ", { {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0], [1, 0, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 326, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 0]]} "For the class ", { {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 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], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 327, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 1]]} {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]]} "For the class ", { {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0], [1, 0, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 328, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {[0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 329, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 0]]} "For the class ", { {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [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, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 330, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {[0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 331, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]]} "For the class ", { {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0], [1, 0, 0]}], [[2, 1], {1}, {[0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 332, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]]} "For the class ", { {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {[0, 0, 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, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 333, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]]} "For the class ", { {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0], [1, 0, 0]}], [[2, 1], {1}, {[0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 334, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {[0, 0, 1], [0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 335, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 0]]} "For the class ", { {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 336, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {[0, 0, 1], [0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 337, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]]} {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 0]]} "For the class ", { {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 338, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 0]]} {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 1]]} "For the class ", {{%3, %2, [[2, 3, 1], [1, 0]]}, {%3, %2, %1}, {%3, [[2, 3, 1], [1, 0]], %1}, {%2, [[2, 3, 1], [1, 0]], %1}}, " the pattern set ", {%3, %2, %1}, " has scheme:" %1 := [[3, 1, 2], [0, 1]] %2 := [[2, 1, 3], [1, 0]] %3 := [[1, 3, 2], [0, 1]] {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {[0, 1, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 339, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]]} {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {[0, 1, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 340, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]]} "For the class ", { {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0], [1, 0, 0]}], [[2, 1], {1}, {[0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 341, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 0]]} "For the class ", { {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {[0, 0, 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, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 342, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 1]]} "For the class ", { {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {[1, 1]}], [[1, 2], {1}, {[0, 1, 0], [1, 0, 0]}], [[2, 1], {1}, {[0, 0, 1], [1, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 343, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 1]]} "For the class ", { {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {[0, 0, 1], [0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 344, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 0]]} "For the class ", { {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {[0, 0, 1]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 345, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {[0, 0, 1], [0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 346, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]]} "For the class ", { {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0], [1, 0, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 347, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0], [1, 0, 0]}], [[2, 1], {1}, {[0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 348, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 0]]} {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]]} "For the class ", { {[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {[0, 0, 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, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 349, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0], [1, 0, 0]}], [[2, 1], {1}, {[0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 350, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]]} "For the class ", {{%3, %2, %1}, {%3, %2, [[3, 1, 2], [1, 0]]}, {%3, %1, [[3, 1, 2], [1, 0]]}, {%2, %1, [[3, 1, 2], [1, 0]]}}, " the pattern set ", {%3, %2, %1}, " has scheme:" %1 := [[2, 3, 1], [0, 1]] %2 := [[2, 1, 3], [0, 1]] %3 := [[1, 3, 2], [1, 0]] {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[1, 0, 0]}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 351, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]]} "For the class ", { {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[1, 0, 0]}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 352, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]]} "For the class ", { {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[1, 0, 0]}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 353, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 1]]} "For the class ", { {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {[1, 1]}], [[1, 2], {}, {[0, 1, 1], [1, 0, 0]}], [[2, 1], {1}, {[0, 0, 1], [1, 1, 0]}], [[1, 2, 3], {1}, {[0, 0, 1, 1], [0, 1, 0, 0], [1, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 354, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 0]]} {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]]} "For the class ", { {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0], [1, 0, 0]}], [[2, 1], {1}, {[0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 355, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1], [0, 1, 0]}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 356, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]]} "For the class ", { {[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[1, 0, 0]}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 357, " is:" {{[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]]}} {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 1]]} "For the class ", {{%3, %2, %1}, {%3, %2, [[3, 1, 2], [1, 1]]}, {%3, %1, [[3, 1, 2], [1, 1]]}, {%2, %1, [[3, 1, 2], [1, 1]]}}, " the pattern set ", {%3, %2, %1}, " has scheme:" %1 := [[2, 3, 1], [1, 1]] %2 := [[2, 1, 3], [1, 1]] %3 := [[1, 3, 2], [1, 1]] {[[], {}, {}], [[1], {}, {[1, 1]}], [[1, 2], {1}, {[0, 1, 0], [1, 0, 0]}], [[2, 1], {1}, {[0, 0, 1], [1, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Class ", 358, " is:" {{%6, %5, %4}, {%6, %5, %2}, {%6, %3, %4}, {%6, %3, %2}, {%5, %4, %1}, {%5, %2, %1}, {%3, %4, %1}, {%3, %2, %1}} %1 := [[3, 2, 1], [1, 1]] %2 := [[3, 1, 2], [1, 1]] %3 := [[2, 1, 3], [1, 1]] %4 := [[2, 3, 1], [1, 1]] %5 := [[1, 3, 2], [1, 1]] %6 := [[1, 2, 3], [1, 1]] {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 1]]} "For the class ", {{%3, %2, %1}, {%3, %2, %5}, {%3, %6, %1}, {%3, %6, %5}, {%2, %1, %4}, {%2, %5, %4}, {%6, %1, %4}, {%6, %5, %4}}, " the pattern set ", {%3, %2, %1}, " has scheme:" %1 := [[2, 3, 1], [1, 1]] %2 := [[1, 3, 2], [1, 1]] %3 := [[1, 2, 3], [1, 1]] %4 := [[3, 2, 1], [1, 1]] %5 := [[3, 1, 2], [1, 1]] %6 := [[2, 1, 3], [1, 1]] {[[], {}, {}], [[1], {}, {[0, 2]}], [[1, 2], {1, 2}, {[0, 0, 1], [0, 1, 0], [1, 0, 0]}], [[2, 1], {1}, {[0, 0, 2], [0, 1, 1], [0, 2, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] "" "Out of the ", 358, " equivalence classes ", 354, "(or ", 98.88268156, " %) classes have enumeration schemes." 4, "(or ", 1.117318436, " %) classes do not have enumeration schemes of depth <=", 5, ", with gap vectors of weight <=", 2 "The classes that failed are: " {{{[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]]}}, {{[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]]}}, { {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 0]]}}, { {[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 0]]}}}